Selina Concise Solutions for Chapter 8 Profit, Loss and Discount Class 8 ICSE Mathematics
Exercise 8A
1. Megha bought 10 note-books for Rs.40 and sold them at Rs.4.75 per note-book. Find, her gain percent.
SolutionC.P. of 10 note-books = Rs. 40
S.P. of 10 note-books@ Rs. 4.75 per note-book
= 4.75 × 10
= Rs. 47.50
Gain = S.P. – C.P.
= Rs 47.50 – Rs 40 = Rs 7.50
Gain% = Gain/C.P. × 100
= 7.50/40 × 100
= 750/40%
= 75/4%
= 18 3/4%
2. A fruit-seller buys oranges at 4 for Rs.3 and sells them at 3 for Rs.4 Find his profit percent.
Solution
Let number of oranges bought = 12
[Note: L.C.M. of 4 and 3 = 12]
∴ C.P. of oranges = Rs. ¾ × 12 = Rs. 9
And S.P. of oranges = Rs. 4/3 × 12
= Rs. 16
∴ Profit = 16 – 9
= Rs. 7
Profit % = Profit/C.P. × 100
= 7/9 × 100
= 700/9%
= 77 7/9%
3. A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs.108. Find:
(i) his gain as percent;
(ii) the number of articles sold to make a profit of Rs.75.
Solution
Let number of articles bought = 60
Note: L.C.M of articles bought = 60
Note: L.C.M. of 15 and 12 = 60
∴ C.P. of the articles = Rs. (112.50/15 × 60)
= Rs. (112.50 × 60)/15
= 112.50 × 4
= Rs. 450.00
And S.P. of the articles = Rs. 108/12 × 60
= Rs. 108 × 5
= Rs. 540
(i) Gain = S.P. – C.P.
= Rs. 540 – Rs 450
= Rs. 90
∴ Gain = Gain/C.P. × 100
= 90/450 × 100
= 100/5
= 20%
(ii) To make a profit of Rs. 90, the number of articles needed to be sold = 60
To make a profit of Re. 1 the number of articles needed to be sold = 60/90
To make a profit of Rs. 75, the number of articles needed to be sold = 60/90 × 75
= 4500/90
= 50
4. A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycles for Rs. 207. Find his gain or loss percent.
Solution
Buying price of the old bicycle = Rs. 162
Money spent on repairs = Rs. 18
Real C.P. of the bicycle = 162 + 18 = Rs. 180
S.P. of the bicycle = Rs 207
Profit = S.P. – C.P. = 207 – 162
= Rs. 45
Gain% = Profit/C.P. × 100
= 45/180 × 100
= 100/4
= 25%
5. An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportations, etc. ; find he loss or the gain as percent.
Solution
Cost price = Rs, 4,800
Selling Price = Rs 5,820
Transport etc. charges = Rs. 1,200
Total cost price = Rs. 4,800 + Rs. 1,200 = Rs.6,000
Loss = Rs. 6000 – Rs. 5820
= Rs. 180
∴ Loss % = 180/6000 × 100
= 3%
6. Mohit sold a T.V. for Rs. 3,600; gaining one-sixth of its selling price. Find :
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.
Solution
S.P. of T.V. = Rs. 3,600
Gain = 1/6 of (3600) = 1/6 × 3600
= Rs. 600
(i) Thus gain = Rs. 600
(ii) Cost Price = 3600 – 600
= Rs. 3000
(iii) Gain % = 600/3000 × 100
= 60/3
= 20%
7. By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find :
(i) the loss incured
(ii) the cost price of the goods
(iii) the loss as percent.
Solution
S.P. = Rs. 5,500
Loss = 1/10 of (S.P.) = 1/10 × 5500
= Rs. 550
(i) Loss incurred = Rs. 550
(ii) C.P. = Rs. 5,500 + Rs. 550
= Rs. 6,050
(iii) Loss% = (550 × 100)/6050
= (10 × 100)/110
= 100/11
= 9 1/11%
8. The selling price of a sofa-set is times of its cost price. Find the gain or the loss as percent.
Solution
Let the cost price (C.P.) = 1
S.P. = 1 × 4/5 = 4/5
∴ Loss = 1 – 4/5
= (5 – 4)/5
= 1/5 [∵ Loss = C.P. – S.P.]
∴ Loss% = Loss/C.P. = (1/5)/1 × 100
= 1/5 × 100
= 20%
9. The cost price of an article is times of its selling price. Find the loss or the gain as percent.
Solution
Let S.P. = 1
C.P. = 4/5 × 1 = 4/5
∴ Gain = S.P. – C.P. [∵ Gain = S.P. – C.P.]
= 1 – 4/5
= (5 – 4)/5
= 1/5
∴ Gain % = Gain/C.P. × 100
= (1/5)/(4/5) × 100
= (1/5)/( 4/5) × 100
= 1/5 × 5/4 × 100
= 25%
10. A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?
Solution
Let C.P. of goods = Rs. 100
∴ S.P. of goods = 80/100 × 100
= Rs. 80
Loss = C.P. – S.P.
= Rs. 100 – Rs. 80
= Rs. 20
Loss% = Loss/C.P. × 100
= 20/100 × 100
= 20%
11. The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Solution
Let S.P. of the article = Rs. 100
∴ C.P. of the article = 90/100 × 100
= Rs. 90
Gain = Rs. 100 – Rs. 90
= Rs. 10
Gain % = Gain/C.P. × 100
= 10/90 × 100
= 100/9 %
= 11 1/9%
12. The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.
Solution
Let S.P. of the article = Rs. 100
30% of S.P. = Rs. 30/100 × 100
= Rs. 30
∴ C.P. of the article = 100 – 30 = Rs. 70
Profit = S.P. – C.P.
Rs. 100 – Rs. 70
= Rs. 30
Profit% = Profit/C.P. × 100
= 30/70 × 100
= 300/7%
= 42 6/7%
13. A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.
Solution
C.P. of 300 egg@ 80 paise each = 300 × 80
= 24000 paise
= Rs. 240
No. of eggs which were broken in transaction = 30
Remaining eggs = 300 – 30
= 270
S.P. of eggs @ Rs. 1 each = 270 × 1
= Rs. 270
Gain = S.P. – C.P.
= Rs. 270 – Rs. 240
= Rs. 30
Gain % = Gain/C.P. × 100
= 30/240 × 100
= 100/8 %
= 12.5%
14. A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :
(i) its cc price;
(ii) the loss percent.
Solution
(i) Let C.P. of the bicycle = Rs. x
∴ Loss = Rs. x/10
S.P. = C.P. – Loss
= x – x/10
But, we are given S.P. = Rs. 405
∴ x – x/10 = 405
⇒ (10x – x)/10 = 405
⇒ 9x/10 = 405
⇒ x = 405 × 10/9
⇒ x = 4050/9
⇒ x = 4050/9
⇒ x = 450
∴ C.P. = Rs. 450
(ii) Loss = x/10
= 450/10 ...(Substituting the value of x)
= Rs. 45
Loss % = Loss/C.P. × 100
= 45/450 × 100
= 4500/450 = 10 %
15. A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;
(i) its cost price;
(ii) the profit percent.
Solution
(i) Let C.P. of the radio-set = Rs. x
Gain = Rs. x/9
S.P. = Rs. (x + x/9) = Rs.(9x + x)/9 = Rs. 10x/9
But, we are given S.P. of the radio-set = Rs. 250
∴ 10x/9 = 250
⇒ x = 250 × 9/10
∴ C.P. = Rs. 450
(ii) Loss = x/10
= 450/10 ...(Substituting the value of x)
= Rs. 45
Loss % = Loss/C.P. × 100
= 45/450 × 100
= 4500/450 = 10 %
15. A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;
(i) its cost price;
(ii) the profit percent.
Solution
(i) Let C.P. of the radio-set = Rs. x
Gain = Rs. x/9
S.P. = Rs. (x + x/9) = Rs.(9x + x)/9 = Rs. 10x/9
But, we are given S.P. of the radio-set = Rs. 250
∴ 10x/9 = 250
⇒ x = 250 × 9/10
⇒ x = 25 × 9
⇒ x = 225
∴ C.P. of the radio set = Rs.225
(ii) Profit = Rs. x/9
= Rs. 225/9 ...(Substituting the value of x)
= Rs. 25
Profit% = Profit/C.P. × 100
= 25/225 × 100
= (25 × 100)/225
= 100/9%
= 11 1/9%
∴ C.P. of the radio set = Rs.225
(ii) Profit = Rs. x/9
= Rs. 225/9 ...(Substituting the value of x)
= Rs. 25
Profit% = Profit/C.P. × 100
= 25/225 × 100
= (25 × 100)/225
= 100/9%
= 11 1/9%
Exercise 8 B
1. Find the selling price, if:
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution
(i) C.P. = Rs. 950 Profit = 8%
∴ S.P. = {950 × (100 + 8)}/100
= (950 × 108)/100
= 19 × 54
= Rs. 1026
(ii) C.P. = Rs. 1,300
Loss = 13%
∴ S.P. = {1300 × (100 – 13)}/100
= 13 × 87
= Rs. 1131
2. Find the cost price, if :
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution
(i) S.P. = Rs. 1, 128, Profit = 12%
C.P. = 100/(100 + profit) × S.P.
∴ C.P. = 100/(100 + 12) × 1680
= (100 × 1680)/112
= (25 × 1680)/28
= 25 × 60
= Rs. 1500
(ii) S.P. = Rs. 1,128, Loss = 6%
C.P. = 100/(100 – Loss) × S.P.
∴ C.P. = (100 × 1128)/(100 – 6)
= (100 × 1128)/94
= 100 × 12
= Rs. 1200
3. By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
Solution
S.P. of an article = Rs. 900
Gain = 20%
C.P. = 100/(100 + Gain%) × S.P.
∴ C.P. = 100/(100 + 20) × Rs. 900
= Rs. 100/120 × 900
= Rs. 9000/12
= Rs. 750
Gain = S.P. – C.P.
= Rs. 900 – Rs. 750
= Rs. 150
4. By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
Solution
S.P. of an article = Rs. 704
Loss = 12%
C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 12) × Rs. 704
= Rs. 100/88 × 704
= Rs. 100 × 8
= Rs. 800
Loss = C.P. – S.P.
= Rs. 800 – Rs. 704
= Rs. 96
5. Find the selling price, if :
(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20
(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%
Solution
(i) C.P. = Rs 352
Overheads = Rs. 28
Net C.P. = Rs. 352 + Rs. 28
= Rs. 380
Profit = 20%
We know = S.P. = (100 + Gain%)/100 × C.P.
= (100 + 20)/100 × 380 =
= Rs. 120/100 × 380
= 12 × 38
= Rs. 456
(ii) C.P. = Rs. 576
Overheads = Rs. 44
Net C.P. = Rs. 576 + Rs. 44
= Rs. 620
Loss = 16%
We know :
S.P. = (100 – Loss%)/100 × C.P.
= (100 – 16)/100 × Rs. 620
= Rs. 84/100 × 620
= Rs. 5208/10
= Rs. 520.80
6. If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5 %?
Solution
S.P. = Rs. 637, Loss = 9%
∴ C.P. = (100 × S.P.)/(100 – 9)
= 100/91 × 637
= 100 × 7
= Rs. 700
Profit = 5%
S.P. = (100 + Profit)/100 × C.P.
S.P. = (100 + 5)/100 × 700
= 105 × 7
= 735
7. A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16 %?
Solution
In the first condition,
S.P. of a radio-set = Rs. 605
C.P. = 100/(100 + gain%) × S.P.
= 100/(100 + 10) × Rs. 605
= Rs. 100/110 × 605
= Rs. (100 × 605)/110
= 10 × 55
= Rs. 550
In the second condition:
C.P. = Rs. 550
Gain = 16%
S.P. = (100 + gain%)/100 × C.P.
= (100 + 16)/100 × Rs. 550
= Rs. 116/100 × 550
= Rs. (116 × 550)/100
= 58 × 111
= Rs. 638
∴ Radio should be sold at Rs. 638
8. By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent; if he sells the same sofa-set for Rs.3150.
Solution
In the first condition:
S.P. of a Sofa-set = Rs. 2500
Loss = 20%
∴ C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 20) × Rs. 2500
= Rs. 100/80 × 2500
= Rs. (100 × 2500)/80
= (5 × 2500)/4
= 5 × 625
= Rs. 3125
In the second condition:
S.P. of the sofa-set = Rs. 3150
C.P. of the sofa-set = Rs. 3125
Gain = S.P. – C.P.
= Rs. 3150 – Rs. 3125
= Rs. 25
Gain% = Gain/C.P. × 100
= 25/3125 × 100
= (25 × 100)/3125
= 100/125
= 4/5%
= 0.8%
9. Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution
In the case of first tape – recorder :
S.P. = Rs. 990
Gain = 10%
C.P. = 100/(100 + Gain%) × S.P.
= 100/(100 + 10) × Rs. 990
= Rs. 100/110 × 990
= Rs. 100 × 9
= Rs. 900
In the case of second tape-recorder :
S.P. = Rs. 990
Loss = 10%
C.P. = 100/(100 - Loss%) × S.P.
= 100(100 – 10) × Rs. 990
= 100/90 × 990
= 100 × 11
= Rs. 1100
Total C.P. of both the tape-recorders,
= Rs. 900 + Rs. 1100
= Rs. 2000
Total S.P. of both the tape-recorders = Rs 990 + Rs. 990
= Rs. 1980
Loss on the whole transaction = C.P. – S.P.
= Rs. 2000 – Rs. 1980
= Rs. 20
Loss% = Loss/C.P. × 100
= Rs. 20/Rs. 2000 × 100 – 2/2%
= 1%
10. A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player.
(iii) the total C.P. of both.
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole
Solution
S.P. of tape-recorder = Rs, 2,760
Gain = 15%
(i) C.P. = (100 × S.P.)/115 [C.P. = (100 × S.P.)/(100 + Gain)]
= (100 × 2760)/115
= (20 × 2760)/23
= 20 × 120
= Rs. 2400
(ii) S.P. of C.D. player = Rs. 3,240
[C.P. = 100/(100 – Loss) × S.P.]
= 100/(100 – 10) × 3240
= 100/90 × 3240
= 100 × 36
= Rs. 3600
(iii) Total C.P. Of both = Rs. 2400 + Rs 3600 = Rs. 6000
(iv) Total S.P. of both = Rs. 2760 + Rs. 3240 = Rs. 6000
(v) Since, S.P. = C.P. there is no gain and no loss on the whole.
11. Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh
Solution
Let C.P. of the scooter for Rajesh = Rs 100x
S.P. for Rajesh = (100x × 92)/100 = 92x
This will be C.P. for Rahim = 92x, Gain = 5%
∴ S.P. for Rahim = (92x × 105)/100
= (92x × 21)/20
= (46x × 21)/10
= 966x/10
This will be C.P. for Prem = Rs. 14,490
∴ 966x/10 = 14,490
⇒ x = 14490/966 × 10
= 14490/483 × 5
= 30 × 5
= 150
(i) C.P. of scooter for Rahim = 92x = 92 × 150
= Rs. 13800
S.P. of scooter for Rahim = 966x/10
= 966/10 × 150
= Rs. 966 × 15
= Rs. 14490
(ii) ∴ C.P. of Scooter for Rajesh = 100x = 100 × 150
= Rs. 15000
S.P. of Scooter for Rajesh = 92x = Rs. 92 × 150
= Rs. 13800
12. John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it?
Solution
Mohan paid for the article = Rs. 912
∵ Peter sold the article to Mohan
∴ For Peter :
S.P. = Rs. 912
Loss = 5%
C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 5) × 912
= Rs. (100 × 912)/95
= 20 × 48
= Rs. 960
John sold the same article to Peter
∴ For John:
S.P. = Rs. 960
Profit = 20%
C.P. = 100/(100 + Profit%) × S.P.
= 100/(100 + 20) × Rs. 960
= Rs. 100/120 × 960
= Rs. 100 × 8
= Rs. 800
Hence, John paid for the article = Rs. 800
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution
(i) C.P. = Rs. 950 Profit = 8%
∴ S.P. = {950 × (100 + 8)}/100
= (950 × 108)/100
= 19 × 54
= Rs. 1026
(ii) C.P. = Rs. 1,300
Loss = 13%
∴ S.P. = {1300 × (100 – 13)}/100
= 13 × 87
= Rs. 1131
2. Find the cost price, if :
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution
(i) S.P. = Rs. 1, 128, Profit = 12%
C.P. = 100/(100 + profit) × S.P.
∴ C.P. = 100/(100 + 12) × 1680
= (100 × 1680)/112
= (25 × 1680)/28
= 25 × 60
= Rs. 1500
(ii) S.P. = Rs. 1,128, Loss = 6%
C.P. = 100/(100 – Loss) × S.P.
∴ C.P. = (100 × 1128)/(100 – 6)
= (100 × 1128)/94
= 100 × 12
= Rs. 1200
3. By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
Solution
S.P. of an article = Rs. 900
Gain = 20%
C.P. = 100/(100 + Gain%) × S.P.
∴ C.P. = 100/(100 + 20) × Rs. 900
= Rs. 100/120 × 900
= Rs. 9000/12
= Rs. 750
Gain = S.P. – C.P.
= Rs. 900 – Rs. 750
= Rs. 150
4. By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
Solution
S.P. of an article = Rs. 704
Loss = 12%
C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 12) × Rs. 704
= Rs. 100/88 × 704
= Rs. 100 × 8
= Rs. 800
Loss = C.P. – S.P.
= Rs. 800 – Rs. 704
= Rs. 96
5. Find the selling price, if :
(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20
(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%
Solution
(i) C.P. = Rs 352
Overheads = Rs. 28
Net C.P. = Rs. 352 + Rs. 28
= Rs. 380
Profit = 20%
We know = S.P. = (100 + Gain%)/100 × C.P.
= (100 + 20)/100 × 380 =
= Rs. 120/100 × 380
= 12 × 38
= Rs. 456
(ii) C.P. = Rs. 576
Overheads = Rs. 44
Net C.P. = Rs. 576 + Rs. 44
= Rs. 620
Loss = 16%
We know :
S.P. = (100 – Loss%)/100 × C.P.
= (100 – 16)/100 × Rs. 620
= Rs. 84/100 × 620
= Rs. 5208/10
= Rs. 520.80
6. If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5 %?
Solution
S.P. = Rs. 637, Loss = 9%
∴ C.P. = (100 × S.P.)/(100 – 9)
= 100/91 × 637
= 100 × 7
= Rs. 700
Profit = 5%
S.P. = (100 + Profit)/100 × C.P.
S.P. = (100 + 5)/100 × 700
= 105 × 7
= 735
7. A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16 %?
Solution
In the first condition,
S.P. of a radio-set = Rs. 605
C.P. = 100/(100 + gain%) × S.P.
= 100/(100 + 10) × Rs. 605
= Rs. 100/110 × 605
= Rs. (100 × 605)/110
= 10 × 55
= Rs. 550
In the second condition:
C.P. = Rs. 550
Gain = 16%
S.P. = (100 + gain%)/100 × C.P.
= (100 + 16)/100 × Rs. 550
= Rs. 116/100 × 550
= Rs. (116 × 550)/100
= 58 × 111
= Rs. 638
∴ Radio should be sold at Rs. 638
8. By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent; if he sells the same sofa-set for Rs.3150.
Solution
In the first condition:
S.P. of a Sofa-set = Rs. 2500
Loss = 20%
∴ C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 20) × Rs. 2500
= Rs. 100/80 × 2500
= Rs. (100 × 2500)/80
= (5 × 2500)/4
= 5 × 625
= Rs. 3125
In the second condition:
S.P. of the sofa-set = Rs. 3150
C.P. of the sofa-set = Rs. 3125
Gain = S.P. – C.P.
= Rs. 3150 – Rs. 3125
= Rs. 25
Gain% = Gain/C.P. × 100
= 25/3125 × 100
= (25 × 100)/3125
= 100/125
= 4/5%
= 0.8%
9. Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution
In the case of first tape – recorder :
S.P. = Rs. 990
Gain = 10%
C.P. = 100/(100 + Gain%) × S.P.
= 100/(100 + 10) × Rs. 990
= Rs. 100/110 × 990
= Rs. 100 × 9
= Rs. 900
In the case of second tape-recorder :
S.P. = Rs. 990
Loss = 10%
C.P. = 100/(100 - Loss%) × S.P.
= 100(100 – 10) × Rs. 990
= 100/90 × 990
= 100 × 11
= Rs. 1100
Total C.P. of both the tape-recorders,
= Rs. 900 + Rs. 1100
= Rs. 2000
Total S.P. of both the tape-recorders = Rs 990 + Rs. 990
= Rs. 1980
Loss on the whole transaction = C.P. – S.P.
= Rs. 2000 – Rs. 1980
= Rs. 20
Loss% = Loss/C.P. × 100
= Rs. 20/Rs. 2000 × 100 – 2/2%
= 1%
10. A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player.
(iii) the total C.P. of both.
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole
Solution
S.P. of tape-recorder = Rs, 2,760
Gain = 15%
(i) C.P. = (100 × S.P.)/115 [C.P. = (100 × S.P.)/(100 + Gain)]
= (100 × 2760)/115
= (20 × 2760)/23
= 20 × 120
= Rs. 2400
(ii) S.P. of C.D. player = Rs. 3,240
[C.P. = 100/(100 – Loss) × S.P.]
= 100/(100 – 10) × 3240
= 100/90 × 3240
= 100 × 36
= Rs. 3600
(iii) Total C.P. Of both = Rs. 2400 + Rs 3600 = Rs. 6000
(iv) Total S.P. of both = Rs. 2760 + Rs. 3240 = Rs. 6000
(v) Since, S.P. = C.P. there is no gain and no loss on the whole.
11. Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh
Solution
Let C.P. of the scooter for Rajesh = Rs 100x
S.P. for Rajesh = (100x × 92)/100 = 92x
This will be C.P. for Rahim = 92x, Gain = 5%
∴ S.P. for Rahim = (92x × 105)/100
= (92x × 21)/20
= (46x × 21)/10
= 966x/10
This will be C.P. for Prem = Rs. 14,490
∴ 966x/10 = 14,490
⇒ x = 14490/966 × 10
= 14490/483 × 5
= 30 × 5
= 150
(i) C.P. of scooter for Rahim = 92x = 92 × 150
= Rs. 13800
S.P. of scooter for Rahim = 966x/10
= 966/10 × 150
= Rs. 966 × 15
= Rs. 14490
(ii) ∴ C.P. of Scooter for Rajesh = 100x = 100 × 150
= Rs. 15000
S.P. of Scooter for Rajesh = 92x = Rs. 92 × 150
= Rs. 13800
12. John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it?
Solution
Mohan paid for the article = Rs. 912
∵ Peter sold the article to Mohan
∴ For Peter :
S.P. = Rs. 912
Loss = 5%
C.P. = 100/(100 – Loss%) × S.P.
= 100/(100 – 5) × 912
= Rs. (100 × 912)/95
= 20 × 48
= Rs. 960
John sold the same article to Peter
∴ For John:
S.P. = Rs. 960
Profit = 20%
C.P. = 100/(100 + Profit%) × S.P.
= 100/(100 + 20) × Rs. 960
= Rs. 100/120 × 960
= Rs. 100 × 8
= Rs. 800
Hence, John paid for the article = Rs. 800
Exercise 8 C
1. A stationer buys pens at 5 for Rs.28 and sells them at a profit of 25 %. How much should a customer pay; if he buys
(i) only one pen ;
(ii) three pens?
Solution
For Stationer:
C.P. of 5 pens = Rs. 28
C.P. of 1 pen = Rs.28/5 = Rs. 5.60
Profit = 25%
∴ S.P. of 1 pen = (100 + Profit%)/100 × C.P. of 1 Pen
= (100 + 25)/100 × Rs. 5.60
= Rs. 125/100 × 5.60
= Rs. (125 × 5.6)/100
= Rs. 5 × 1.4
= Rs 7
S.P. of 3 pens = 3 × 7 = Rs. 21
∴ Customer pays for
(i) only one pen = Rs. 7
(ii) Three pens = Rs. 21
2. A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :
(i) C.P. of 4 oranges,
(ii) C.P. of one orange.
(iii) S.P. of one orange.
(iv) profit made by selling one orange.
(v) number of oranges brought and sold in order to gain Rs. 24.
Solution
S.P. of 4 oranges = Rs. 3
∴ S.P. of 1 orange = Rs. ¾, Gain = 50%
S.P. = (C.P. × 150)/100
∴ C.P. of 1 orange = (100 × S.P.)/(100 + 50)
= (100 × ¾)/150
= 75/150
= Re ½
(i) C.P. of 4 oranges = 4 ×1/2 = Rs. 2
(ii) C.P. of 1 oranges = Rs. ½ = Rs. (0.50)
(iii) S.P. of 1 orange = Rs. ¾ = Rs. 0.75
(iv) Profit made by selling one orange = Rs. ¾ - Rs. ½
= Rs. ¼
= Rs. 0.25
(v) If gain is Rs. ¼; number of oranges = 1
If gain is Rs. 24, number of oranges = (1/1)/4 × 24
= 1 × 4/1 × 24
= 96
3. A man sells 12 articles for Rs. 80 gaining 33%. Find the number of articles bought by the man for Rs. 90.
Solution
S.P. of 12 articles = Rs. 80,
Gain = 33 1/3% = 100/3%
C.P. = 100/(100 + Gain) × S.P.
= 100/(100 + 100/3) × 80
= 100/{(300 + 100)/3} × 80
= 100/(400/3) × 80
= 100 × 3/400 × 80
= Rs. 60
Rs. 60 is the cost of 12 articles
Re. 1 is the cost of = 12/60 article
Rs. 90 is the cost of = 12/60 × 90
= 1/5 × 90 = 18
Man can buy article for Rs. 90 = 18
4. The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
Solution
C.P. of 20 articles = S.P. of 16 articles.
Let C.P. of 1 article = Re. 1
C.P. of 20 articles = Rs.20
and C.P. of 16 articles = Rs.16
S.P. of 16 articles = Rs.20
[S.P. of 16 articles = C.P. of 20 articles]
Gain = Rs.20 – Rs.16 = Rs.4
Gain% = 4/16 × 100
= (4/16 × 100)
= 25%
5. The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
Solution
S.P. of 15 articles = C.P. of 12 articles
Let C.P. of 1 article = Re.1
C.P. of 12 article = Rs.12
and C.P. of 15 articles = Rs.15
S.P. of 15 articles = Rs.12
[S.P. of 15 articles = C.P. of 12 articles]
Loss = Rs.15 – Rs.12 = Rs.3
Loss% = 3/15 × 100 = 20%
6. By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
Solution
Let C.P. of 1 pen = Re.1
C.P. of 2 pens = Rs.2
and C.P. of 8 pens = Rs.8
Loss = Rs.2 ...[Loss = C.P. of 2 Pens]
Loss% = 2/8 × 100 = 25%
7. A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
If he desires a profit of 12% on the whole; find :
(i) the selling price of the rest of the rice ;
(ii) the percentage profit on the rest of the rice.
Solution
C.P. of the rice = Rs. 4500
Profit desired on the whole = 12%
∴ S.P. of the whole rice = (100 + gain%)/100 × C.P.
= (100 + 12)/100 × Rs. 4500
= Rs. 112/100 × 4500
= 112 × 45
= Rs. 5040
C.P. of 1/3 of rice = 1/3 × Rs. 4500
= Rs. 1500
Since, gain on 1/3 of rice = 10%
∴ S.P. on it = (100 + gain%)/100 × C.P.
= (100 + 10)/100 × Rs. 1500
= Rs. 110/100 × 1500
= 11 × 150
= Rs. 1650
Remaining C.P. of the Rice = Rs. 4500 – Rs. 1500
= Rs. 3000
Remaining S.P. of the rice = Rs. 5040 – Rs. 1650
= Rs. 3390
Profit on the remaining rice = Rs. 3390 – Rs. 3000
= Rs. 390
Gain% on the remaining rice = 390/3000 × 100
= (390 × 100)/3000
= 13%
(i) ∴ S.P. of the rest of the Price = Rs. 3390
(ii) % Profit on the rest of the rice = 13%
8. Mohan bought a certain number of note-books for Rs.600. He sold of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole?
Solution
C.P. of note books = Rs. 600
Gain desired on the whole = 10%
∴ Total S.P. of all the note-books = (100 + gain%)/100 × C.P.
= (100 + 10)/100 × Rs. 600
= Rs. 110/100 × 600
= Rs. 660
C.P. of ¼ of the note-books = ¼ × Rs. 600
= Rs. 150
Loss on these note-books = 5%
∴ S.P. of these note-books = (100 – Loss%)/100 × C.P.
= (100 – 5)/100 × Rs. 150
= Rs. 95/100 × 150
= Rs. 14250/100
= Rs. 142.50
Now, C.P. of the remaining note-books = Rs. 600 – Rs. 150
= Rs. 450
Required S.P. of the remaining note-books = Rs. 660 – Rs. 142.50
= Rs. 517. 50
9. Raju sells a watch at 5% profit. Had he sold it for Rs.24 more; he would have gained 11%. Find the cost price of the watch.
Solution
Let C.P. of the watch = Rs.100
When profit = 5%;
S.P. = Rs.(100 + 5) = Rs.105
When profit = 11%;
S.P. = Rs.(100 + 11) = Rs .111
Difference of two selling prices = Rs. 111 – Rs. 105 = Rs.6
When watch sold for Rs.6 more; then C.P. of the watch = Rs.100
When watch sold for Re. 1 more; then C.P. of the watch = Rs. 100/6
When watch sold for Rs.24 more; then C.P. of the watch = Rs. 100/6 × 24 = Rs.400
Question 10: A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
Solution 10:
Let C.P. of the bicycle = Rs.100
In the I case :
When Profit = 5% ;
S.P. = Rs. (100 + 5) = Rs. 105
In the II case:
C.P. = (100 – 30/100 × 100)
= Rs. (100 – 30)
= Rs. 70
Profit = 30%
S.P. = (100 + Profit)/100 × C.P.
= (100 + 30)/100 × Rs. 70
= 130/100 × Rs. 70
= Rs. (130 × 70)/100
= Rs. 91
Difference of two selling prices = Rs. 105 – Rs. 91
= Rs. 14
If difference is Rs. 14 then C.P. of the bicycle = Rs. 100
If difference is Re. 1 then C.P. of the bicycle = Rs. 100/14
If difference is Rs. 63 then C.P. of the bicycle = Rs. 100/14 × 63
= Rs. (100 × 63)/14
= Rs. 50 × 9
= Rs. 450
(i) only one pen ;
(ii) three pens?
Solution
For Stationer:
C.P. of 5 pens = Rs. 28
C.P. of 1 pen = Rs.28/5 = Rs. 5.60
Profit = 25%
∴ S.P. of 1 pen = (100 + Profit%)/100 × C.P. of 1 Pen
= (100 + 25)/100 × Rs. 5.60
= Rs. 125/100 × 5.60
= Rs. (125 × 5.6)/100
= Rs. 5 × 1.4
= Rs 7
S.P. of 3 pens = 3 × 7 = Rs. 21
∴ Customer pays for
(i) only one pen = Rs. 7
(ii) Three pens = Rs. 21
2. A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :
(i) C.P. of 4 oranges,
(ii) C.P. of one orange.
(iii) S.P. of one orange.
(iv) profit made by selling one orange.
(v) number of oranges brought and sold in order to gain Rs. 24.
Solution
S.P. of 4 oranges = Rs. 3
∴ S.P. of 1 orange = Rs. ¾, Gain = 50%
S.P. = (C.P. × 150)/100
∴ C.P. of 1 orange = (100 × S.P.)/(100 + 50)
= (100 × ¾)/150
= 75/150
= Re ½
(i) C.P. of 4 oranges = 4 ×1/2 = Rs. 2
(ii) C.P. of 1 oranges = Rs. ½ = Rs. (0.50)
(iii) S.P. of 1 orange = Rs. ¾ = Rs. 0.75
(iv) Profit made by selling one orange = Rs. ¾ - Rs. ½
= Rs. ¼
= Rs. 0.25
(v) If gain is Rs. ¼; number of oranges = 1
If gain is Rs. 24, number of oranges = (1/1)/4 × 24
= 1 × 4/1 × 24
= 96
3. A man sells 12 articles for Rs. 80 gaining 33%. Find the number of articles bought by the man for Rs. 90.
Solution
S.P. of 12 articles = Rs. 80,
Gain = 33 1/3% = 100/3%
C.P. = 100/(100 + Gain) × S.P.
= 100/(100 + 100/3) × 80
= 100/{(300 + 100)/3} × 80
= 100/(400/3) × 80
= 100 × 3/400 × 80
= Rs. 60
Rs. 60 is the cost of 12 articles
Re. 1 is the cost of = 12/60 article
Rs. 90 is the cost of = 12/60 × 90
= 1/5 × 90 = 18
Man can buy article for Rs. 90 = 18
4. The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
Solution
C.P. of 20 articles = S.P. of 16 articles.
Let C.P. of 1 article = Re. 1
C.P. of 20 articles = Rs.20
and C.P. of 16 articles = Rs.16
S.P. of 16 articles = Rs.20
[S.P. of 16 articles = C.P. of 20 articles]
Gain = Rs.20 – Rs.16 = Rs.4
Gain% = 4/16 × 100
= (4/16 × 100)
= 25%
5. The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
Solution
S.P. of 15 articles = C.P. of 12 articles
Let C.P. of 1 article = Re.1
C.P. of 12 article = Rs.12
and C.P. of 15 articles = Rs.15
S.P. of 15 articles = Rs.12
[S.P. of 15 articles = C.P. of 12 articles]
Loss = Rs.15 – Rs.12 = Rs.3
Loss% = 3/15 × 100 = 20%
6. By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
Solution
Let C.P. of 1 pen = Re.1
C.P. of 2 pens = Rs.2
and C.P. of 8 pens = Rs.8
Loss = Rs.2 ...[Loss = C.P. of 2 Pens]
Loss% = 2/8 × 100 = 25%
7. A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
If he desires a profit of 12% on the whole; find :
(i) the selling price of the rest of the rice ;
(ii) the percentage profit on the rest of the rice.
Solution
C.P. of the rice = Rs. 4500
Profit desired on the whole = 12%
∴ S.P. of the whole rice = (100 + gain%)/100 × C.P.
= (100 + 12)/100 × Rs. 4500
= Rs. 112/100 × 4500
= 112 × 45
= Rs. 5040
C.P. of 1/3 of rice = 1/3 × Rs. 4500
= Rs. 1500
Since, gain on 1/3 of rice = 10%
∴ S.P. on it = (100 + gain%)/100 × C.P.
= (100 + 10)/100 × Rs. 1500
= Rs. 110/100 × 1500
= 11 × 150
= Rs. 1650
Remaining C.P. of the Rice = Rs. 4500 – Rs. 1500
= Rs. 3000
Remaining S.P. of the rice = Rs. 5040 – Rs. 1650
= Rs. 3390
Profit on the remaining rice = Rs. 3390 – Rs. 3000
= Rs. 390
Gain% on the remaining rice = 390/3000 × 100
= (390 × 100)/3000
= 13%
(i) ∴ S.P. of the rest of the Price = Rs. 3390
(ii) % Profit on the rest of the rice = 13%
8. Mohan bought a certain number of note-books for Rs.600. He sold of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole?
Solution
C.P. of note books = Rs. 600
Gain desired on the whole = 10%
∴ Total S.P. of all the note-books = (100 + gain%)/100 × C.P.
= (100 + 10)/100 × Rs. 600
= Rs. 110/100 × 600
= Rs. 660
C.P. of ¼ of the note-books = ¼ × Rs. 600
= Rs. 150
Loss on these note-books = 5%
∴ S.P. of these note-books = (100 – Loss%)/100 × C.P.
= (100 – 5)/100 × Rs. 150
= Rs. 95/100 × 150
= Rs. 14250/100
= Rs. 142.50
Now, C.P. of the remaining note-books = Rs. 600 – Rs. 150
= Rs. 450
Required S.P. of the remaining note-books = Rs. 660 – Rs. 142.50
= Rs. 517. 50
9. Raju sells a watch at 5% profit. Had he sold it for Rs.24 more; he would have gained 11%. Find the cost price of the watch.
Solution
Let C.P. of the watch = Rs.100
When profit = 5%;
S.P. = Rs.(100 + 5) = Rs.105
When profit = 11%;
S.P. = Rs.(100 + 11) = Rs .111
Difference of two selling prices = Rs. 111 – Rs. 105 = Rs.6
When watch sold for Rs.6 more; then C.P. of the watch = Rs.100
When watch sold for Re. 1 more; then C.P. of the watch = Rs. 100/6
When watch sold for Rs.24 more; then C.P. of the watch = Rs. 100/6 × 24 = Rs.400
Question 10: A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
Solution 10:
Let C.P. of the bicycle = Rs.100
In the I case :
When Profit = 5% ;
S.P. = Rs. (100 + 5) = Rs. 105
In the II case:
C.P. = (100 – 30/100 × 100)
= Rs. (100 – 30)
= Rs. 70
Profit = 30%
S.P. = (100 + Profit)/100 × C.P.
= (100 + 30)/100 × Rs. 70
= 130/100 × Rs. 70
= Rs. (130 × 70)/100
= Rs. 91
Difference of two selling prices = Rs. 105 – Rs. 91
= Rs. 14
If difference is Rs. 14 then C.P. of the bicycle = Rs. 100
If difference is Re. 1 then C.P. of the bicycle = Rs. 100/14
If difference is Rs. 63 then C.P. of the bicycle = Rs. 100/14 × 63
= Rs. (100 × 63)/14
= Rs. 50 × 9
= Rs. 450
11. Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs.36 more; she would have gained 20%. Find the cost price of the article.
Solution
Let C.P. of the article = Rs. 100
In the I case : When loss = 8%
S.P. = Rs. (100 – 8)
= Rs. 92
In the II case: C.P. = Rs. (100 – 10/100 × 100)
= Rs. (100 – 10)
= Rs. 90
Profit = 20%
S.P. = (100 + 20)/100 × C.P.
= 120/100 × Rs. 90
= Rs. 12 × 9
= Rs. 108
Difference of two selling prices = Rs. 108 – Rs. 92
= Rs. 16
If the difference of two selling prices is Rs. 16 then C.P. = Rs 100
If the difference of two selling prices is Re. 1 then C.P. = Rs 100/16
If the difference of two selling prices is Rs. 36 then C.P. = Rs 100/16 × 36
= Rs. (100 × 36)/16
= Rs. 25 × 9
= Rs. 225
Solution
Let C.P. of the article = Rs. 100
In the I case : When loss = 8%
S.P. = Rs. (100 – 8)
= Rs. 92
In the II case: C.P. = Rs. (100 – 10/100 × 100)
= Rs. (100 – 10)
= Rs. 90
Profit = 20%
S.P. = (100 + 20)/100 × C.P.
= 120/100 × Rs. 90
= Rs. 12 × 9
= Rs. 108
Difference of two selling prices = Rs. 108 – Rs. 92
= Rs. 16
If the difference of two selling prices is Rs. 16 then C.P. = Rs 100
If the difference of two selling prices is Re. 1 then C.P. = Rs 100/16
If the difference of two selling prices is Rs. 36 then C.P. = Rs 100/16 × 36
= Rs. (100 × 36)/16
= Rs. 25 × 9
= Rs. 225
Exercise 8 D
1. An article is marked for Rs. 1,300 and is sold for Rs. 1,144; find the discount percent.
Solutions
Marked price = Rs. 1,300 , S.P. = Rs. 1,144
Discount = Rs. 1,300 – Rs. 1,114
= Rs. 156
∴ Discount % = 156/1300 × 100
= 156/13
= 12%
2. The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution
Marked Price = Rs. 23,600, Discount = 8%
∴ S.P. = 23,600 × (100 – 8)/100
= 236 × 92
= Rs. 21, 712
3. A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400; find the discount given and the selling price of the watch.
Solution
List price of the watch = Rs. 1,400
Discount = 9%
Discount = (1400 x 9)/100 = 14 x 9 = Rs. 126
S.P. = (List price – Discount) = Rs. (1400 – 126) = Rs. 1274
4. A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution
S.P. of the article = Rs. 248.50
Discount = 10%
Let M.P. = Rs. 100
Discount = 10/100 × Rs. 100
= Rs. 10
Selling Price = Rs. 100 – Rs. 10
= Rs. 90
If S.P. is Rs. 90; then M.P. = Rs.100
If S.P. is Re 1; then M.P. = Rs.100/90
If S.P. is Rs. 248.50; then M.P. = Rs.100/90 × 248.50
= Rs. (100 × 248.50)/90
= Rs. 24850/90
= Rs. 276.11(Approx.)
5. A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :
(i) the marked price of the article.
(ii) the selling price, if he sells the articles at 10 percent discount.
(iii) the percentage discount given by him, if he sells the article for Rs.496.80
Solution
C.P. of the article = Rs. 450
(i) Marked price of the article = (100 + 20)/100 × Rs. 450
= Rs. 120/100 × 450
= 12 × 45
= Rs. 540
(ii) Discount = 10/100 × M.P.
= 10/100 × Rs. 540
= Rs. 54
S.P. = M.P. – Discount
= Rs. 540 – Rs. 54
Rs. 486
(iii) S.P. = Rs. 496.80
M.P. = Rs. 540
Discount = M.P. – S.P.
= Rs. 540 – Rs. 496.80
= Rs. 43.20
Discount % = Discount/M.P. × 100
= 43.20/540 × 100
= 4320/540 %
= 8%
Solutions
Marked price = Rs. 1,300 , S.P. = Rs. 1,144
Discount = Rs. 1,300 – Rs. 1,114
= Rs. 156
∴ Discount % = 156/1300 × 100
= 156/13
= 12%
2. The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution
Marked Price = Rs. 23,600, Discount = 8%
∴ S.P. = 23,600 × (100 – 8)/100
= 236 × 92
= Rs. 21, 712
3. A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400; find the discount given and the selling price of the watch.
Solution
List price of the watch = Rs. 1,400
Discount = 9%
Discount = (1400 x 9)/100 = 14 x 9 = Rs. 126
S.P. = (List price – Discount) = Rs. (1400 – 126) = Rs. 1274
4. A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution
S.P. of the article = Rs. 248.50
Discount = 10%
Let M.P. = Rs. 100
Discount = 10/100 × Rs. 100
= Rs. 10
Selling Price = Rs. 100 – Rs. 10
= Rs. 90
If S.P. is Rs. 90; then M.P. = Rs.100
If S.P. is Re 1; then M.P. = Rs.100/90
If S.P. is Rs. 248.50; then M.P. = Rs.100/90 × 248.50
= Rs. (100 × 248.50)/90
= Rs. 24850/90
= Rs. 276.11(Approx.)
5. A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :
(i) the marked price of the article.
(ii) the selling price, if he sells the articles at 10 percent discount.
(iii) the percentage discount given by him, if he sells the article for Rs.496.80
Solution
C.P. of the article = Rs. 450
(i) Marked price of the article = (100 + 20)/100 × Rs. 450
= Rs. 120/100 × 450
= 12 × 45
= Rs. 540
(ii) Discount = 10/100 × M.P.
= 10/100 × Rs. 540
= Rs. 54
S.P. = M.P. – Discount
= Rs. 540 – Rs. 54
Rs. 486
(iii) S.P. = Rs. 496.80
M.P. = Rs. 540
Discount = M.P. – S.P.
= Rs. 540 – Rs. 496.80
= Rs. 43.20
Discount % = Discount/M.P. × 100
= 43.20/540 × 100
= 4320/540 %
= 8%
6. The list price of an article is Rs.800 and is available at a discount of 15 percent. Find :
(i) selling price of the article ;
(ii) cost price of the article, if a profit of 13 % is made on selling it.
Solution
List price of the article = Rs. 800
Discount @ 15% = 15/100 × Rs. 800
(i) S.P. of the article = RS. 800 – Rs. 120
= Rs. 680
(ii) S.P. of the article = Rs. 680
Profit = 13 1/3%
= 40/3 %
C.P. = 100/(100 + Profit %) × S.P.
= 100/(100 + 40/3) × Rs. 680
= 100/340/3 × Rs. 680
= 3/340 × 100 × 680
= 3 × 100 × Rs. 2
= Rs. 600
7. An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution
(i) Market Price = Rs. 2,250
S.P. = {2250(100 – 12)}/100
= (2250 × 88)/100
= 45 × 44
= Rs. 1980
(ii) S.P. = Rs. 1980, Profit = 10%
∴ C.P. of the article = 100/110 × 1980
= 100 × 18
= Rs. 1800
8. By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440; find :
(i) the marked price of the article.
(ii) the cost price of the article.
Solution
S.P. of the article = Rs. 1440
Let marked Price = Rs. 100x
Discount = 20%
∴ S.P. = {100x(100 – 20)/100}
= 80x
According to statement, 80x = 1440
x = 1440/80 ⇒ x =18
∴ x = 18
∴ Marked price = 100x = 100 × 18
= Rs. 1800
S.P. = Rs. 1440
Profit = 25%
∴ C.P. = (100 × S.P.)/(100 + 25)
= (100 × 1440)/125
= 4/5 × 1440
= 4 × 288
= Rs. 1152
9. A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
Solution
Let C.P. of the goods = Rs. 100
M.P. of the goods = Rs 100 + Rs. 30
= Rs. 130
Discount = 10/100 × Rs. 130
= Rs. 1300/100
= Rs. 13
S.P. of the goods = M.P. – Discount
= Rs 130 – Rs. 13
= Rs. 117
Gain = S.P. – C.P.
= Rs. 117 – Rs. 100
= Rs. 17
Gain% = Gain/C.P. × 100
= 17/100 × 100
= 177%
10. A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.
Solution
C.P. of the dress = Rs. 400
Profit = 20/100 × Rs. 400
= Rs. 80
S.P. = C.P. + Profit
= Rs. 400 + Rs. 80
= Rs. 480
Let, M.P. of the dress = Rs. 100
Discount @ 20% = 20/100 × Rs. 100
= Rs. 20
S.P. of the dress = M.P. – Discount
= Rs. 100 – Rs. 20
= Rs. 80
If S.P. of the dress is ₹ 80; then M.P. = ₹ 100
If S.P. of the dress is ₹ 1 then M.P. = ₹ 100/80
If S.P. of the dress is ₹ 480 then M.P. = ₹ 100/80 × 480
= ₹ 100 × 6 = 600
∴ M.P. of the dress = ₹ 600
11. At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution
Let marked price = ₹100x
Discount = 12%
∴ S.P. = {100x(100 – 12)}/100
= (100x × 88)/100
= 88x
According to statement,
88x = 13.20
∴ x = 13.20/88 = 1320/(88 × 100)
= 30/200
= 3/20
∴ Marked price 100x = (100 × 3)/ 20
= ₹ 15
New S.P. = (15 × 95)/20 [∵ discount = 5%]
= (15 × 19)/20
= (3 × 19)/4
= 57/4
= ₹ 14.25
12. The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.
Solution
C.P. = ₹ 2, 400
∴ Marked Price = 2400(100 + 25)/100
= 24 × 125
= ₹ 3000
Discount = 15%
∴ S.P. = 3000 × (100 – 15)/100 = 30 × 85 = ₹ 2550
∴ Profit = ₹2550 – ₹ 2400
= ₹ 150
Profit% = 150/2400 × 100
= 50/8
= 25/4
= 6 ¼%
13. Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?
Solution
C.P of one article = ₹ 450
C.P. of 30 articles = ₹ 450 × 30
= ₹ 13500
C.P. of 1/3 articles = ₹ 450 × 30/3
= ₹ 4500
Loss of = 6%
∴ S.P. of 10 articles = C.P. × (100 – Loss%)/100
= ₹{4500 × (100 – 6)}/100
= ₹(4500 × 94)/100
= ₹ 4230
C.P. of remaining articles = ₹ 4500 × 20
= ₹9000
Profit on the whole = 10%
∴ Total S.P. of 30 articles = ₹(13500 × (100 + 10)/100
= ₹(13500 × 110)/100
= ₹14850
∴ S.P. of remaining 20 articles = ₹14850 - ₹ 10620
∴ S.P. of 1 article = ₹10620/20
= ₹531
14. The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:
(i) Its marked price
(ii) its selling price
(iii) the profit percent.
Solution
Let M.P. of an article = ₹100
∴ Cost Price = 100 × (100 – 25)/100
= ₹ (100 × 75)/100
= ₹ 75
Discount = 15%
∴ S.P. = ₹ 100 - ₹ 15 = ₹ 85
But cost price = ₹2400
(i) ∴ Marked price = ₹2400 × 100/75
= ₹32 × 100
= ₹3200
(ii) and S.P. = ₹(3200 × 85)/100
= ₹2720
(iii) Profit = S.P. – C.P.
= ₹ 2720 – 2400
= ₹ 320
∴ Profit % = (Profit × 100)/C.P.
= (320 × 100)/2400
= 40/3%
= 13 1/3%
15. Find a single discount (as percent) equivalent to following successive discounts:
(i) 20% and 12%
(ii) 10%, 20% and 20%
(iii) 20%, 10% and 5%
Solution
(i) Successive discount = 20% and 12%
Let M.P. = ₹ 100
First discount = 20%
Second discount = 12%
∴ S.P. = M.P.(100 – Discount%)/100
= {100 × (100 – 20)(100 – 12)/(100 × 100)
= (100 × 80 × 88)/(100 × 100)
= 352/5
∴ Total discount on ₹ 100 = 100 – 352/5
= (500 – 352)/5
= ₹148/5
∴ Single discount = 148/5%
= 29 3/5%
(ii) Successive discounts 10%, 20% and 20%
Let M.P. = ₹100
∴ S.P. after 3 discounts = {100(100 – 10)(100 – 20)(100 – 20)}/(100 × 100 × 100)
= (100 × 90 × 80 × 80)/(100 × 100 × 100)
= 576/10
∴ Total discount = ₹100 – 576/10
= ₹(1000 – 576)/10
= 424/10
∴ Single discount = 424/10% = 42.4%
(iii) Successive discounts = 20%, 10%, 5%
Let M.P. = ₹ 100
∴ S.P. after three discounts = ₹{100(100 – 20)(100 – 10)(100 – 5)/(100 × 100 × 100)
= ₹(100 × 80 × 90 × 95)/(100 × 100 × 100)
= ₹342/5
∴ Total discount = 100 - 342/5
= (500 – 352)/5
= 158/5
∴ Single discount = 158/5 % = 31.6%
16. Find the single discount (as percent) equivalent to successive discounts of:
(i) 80% and 80%
(ii) 60% and 60%
(iii) 60% and 80%
Solution
(i) Successive discounts = 80% and 80%
Let M.P. = ₹100
Then S.P. after two discounts = ₹{100 (100 – 80)(100 – 80)/(100 × 100)
= (100 × 20 × 20)/(100 × 100)
= ₹4
∴ Total discounts = ₹ 100 – 4 = ₹96
∴ Single discount = 96%
(ii) Successive discounts = 60% and 60%
Let M.P. = ₹100
Then S.P. after two discounts, = {100(100 – 60)(100 – 60)/(100 × 100)
= (100 × 40 × 40)/(100 × 100)
= ₹16
∴ Total discount = ₹ 100 – 16 = ₹84
Single discount = 84 %
(iii) Successive discounts = 60% and 80%
let M.P. = ₹ 100
∴ S.P. after two discounts = ₹{100(100 - 60)(100 - 80)/(100 × 100)
= ₹(100 × 40 × 20)/(100 × 100)
= ₹ 8
∴ Total discount = ₹ 100 – 8 = ₹92
∴ Single discount = 92%
(i) selling price of the article ;
(ii) cost price of the article, if a profit of 13 % is made on selling it.
Solution
List price of the article = Rs. 800
Discount @ 15% = 15/100 × Rs. 800
(i) S.P. of the article = RS. 800 – Rs. 120
= Rs. 680
(ii) S.P. of the article = Rs. 680
Profit = 13 1/3%
= 40/3 %
C.P. = 100/(100 + Profit %) × S.P.
= 100/(100 + 40/3) × Rs. 680
= 100/340/3 × Rs. 680
= 3/340 × 100 × 680
= 3 × 100 × Rs. 2
= Rs. 600
7. An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution
(i) Market Price = Rs. 2,250
S.P. = {2250(100 – 12)}/100
= (2250 × 88)/100
= 45 × 44
= Rs. 1980
(ii) S.P. = Rs. 1980, Profit = 10%
∴ C.P. of the article = 100/110 × 1980
= 100 × 18
= Rs. 1800
8. By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440; find :
(i) the marked price of the article.
(ii) the cost price of the article.
Solution
S.P. of the article = Rs. 1440
Let marked Price = Rs. 100x
Discount = 20%
∴ S.P. = {100x(100 – 20)/100}
= 80x
According to statement, 80x = 1440
x = 1440/80 ⇒ x =18
∴ x = 18
∴ Marked price = 100x = 100 × 18
= Rs. 1800
S.P. = Rs. 1440
Profit = 25%
∴ C.P. = (100 × S.P.)/(100 + 25)
= (100 × 1440)/125
= 4/5 × 1440
= 4 × 288
= Rs. 1152
9. A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
Solution
Let C.P. of the goods = Rs. 100
M.P. of the goods = Rs 100 + Rs. 30
= Rs. 130
Discount = 10/100 × Rs. 130
= Rs. 1300/100
= Rs. 13
S.P. of the goods = M.P. – Discount
= Rs 130 – Rs. 13
= Rs. 117
Gain = S.P. – C.P.
= Rs. 117 – Rs. 100
= Rs. 17
Gain% = Gain/C.P. × 100
= 17/100 × 100
= 177%
10. A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.
Solution
C.P. of the dress = Rs. 400
Profit = 20/100 × Rs. 400
= Rs. 80
S.P. = C.P. + Profit
= Rs. 400 + Rs. 80
= Rs. 480
Let, M.P. of the dress = Rs. 100
Discount @ 20% = 20/100 × Rs. 100
= Rs. 20
S.P. of the dress = M.P. – Discount
= Rs. 100 – Rs. 20
= Rs. 80
If S.P. of the dress is ₹ 80; then M.P. = ₹ 100
If S.P. of the dress is ₹ 1 then M.P. = ₹ 100/80
If S.P. of the dress is ₹ 480 then M.P. = ₹ 100/80 × 480
= ₹ 100 × 6 = 600
∴ M.P. of the dress = ₹ 600
11. At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution
Let marked price = ₹100x
Discount = 12%
∴ S.P. = {100x(100 – 12)}/100
= (100x × 88)/100
= 88x
According to statement,
88x = 13.20
∴ x = 13.20/88 = 1320/(88 × 100)
= 30/200
= 3/20
∴ Marked price 100x = (100 × 3)/ 20
= ₹ 15
New S.P. = (15 × 95)/20 [∵ discount = 5%]
= (15 × 19)/20
= (3 × 19)/4
= 57/4
= ₹ 14.25
12. The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.
Solution
C.P. = ₹ 2, 400
∴ Marked Price = 2400(100 + 25)/100
= 24 × 125
= ₹ 3000
Discount = 15%
∴ S.P. = 3000 × (100 – 15)/100 = 30 × 85 = ₹ 2550
∴ Profit = ₹2550 – ₹ 2400
= ₹ 150
Profit% = 150/2400 × 100
= 50/8
= 25/4
= 6 ¼%
13. Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?
Solution
C.P of one article = ₹ 450
C.P. of 30 articles = ₹ 450 × 30
= ₹ 13500
C.P. of 1/3 articles = ₹ 450 × 30/3
= ₹ 4500
Loss of = 6%
∴ S.P. of 10 articles = C.P. × (100 – Loss%)/100
= ₹{4500 × (100 – 6)}/100
= ₹(4500 × 94)/100
= ₹ 4230
C.P. of remaining articles = ₹ 4500 × 20
= ₹9000
Profit on the whole = 10%
∴ Total S.P. of 30 articles = ₹(13500 × (100 + 10)/100
= ₹(13500 × 110)/100
= ₹14850
∴ S.P. of remaining 20 articles = ₹14850 - ₹ 10620
∴ S.P. of 1 article = ₹10620/20
= ₹531
14. The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:
(i) Its marked price
(ii) its selling price
(iii) the profit percent.
Solution
Let M.P. of an article = ₹100
∴ Cost Price = 100 × (100 – 25)/100
= ₹ (100 × 75)/100
= ₹ 75
Discount = 15%
∴ S.P. = ₹ 100 - ₹ 15 = ₹ 85
But cost price = ₹2400
(i) ∴ Marked price = ₹2400 × 100/75
= ₹32 × 100
= ₹3200
(ii) and S.P. = ₹(3200 × 85)/100
= ₹2720
(iii) Profit = S.P. – C.P.
= ₹ 2720 – 2400
= ₹ 320
∴ Profit % = (Profit × 100)/C.P.
= (320 × 100)/2400
= 40/3%
= 13 1/3%
15. Find a single discount (as percent) equivalent to following successive discounts:
(i) 20% and 12%
(ii) 10%, 20% and 20%
(iii) 20%, 10% and 5%
Solution
(i) Successive discount = 20% and 12%
Let M.P. = ₹ 100
First discount = 20%
Second discount = 12%
∴ S.P. = M.P.(100 – Discount%)/100
= {100 × (100 – 20)(100 – 12)/(100 × 100)
= (100 × 80 × 88)/(100 × 100)
= 352/5
∴ Total discount on ₹ 100 = 100 – 352/5
= (500 – 352)/5
= ₹148/5
∴ Single discount = 148/5%
= 29 3/5%
(ii) Successive discounts 10%, 20% and 20%
Let M.P. = ₹100
∴ S.P. after 3 discounts = {100(100 – 10)(100 – 20)(100 – 20)}/(100 × 100 × 100)
= (100 × 90 × 80 × 80)/(100 × 100 × 100)
= 576/10
∴ Total discount = ₹100 – 576/10
= ₹(1000 – 576)/10
= 424/10
∴ Single discount = 424/10% = 42.4%
(iii) Successive discounts = 20%, 10%, 5%
Let M.P. = ₹ 100
∴ S.P. after three discounts = ₹{100(100 – 20)(100 – 10)(100 – 5)/(100 × 100 × 100)
= ₹(100 × 80 × 90 × 95)/(100 × 100 × 100)
= ₹342/5
∴ Total discount = 100 - 342/5
= (500 – 352)/5
= 158/5
∴ Single discount = 158/5 % = 31.6%
16. Find the single discount (as percent) equivalent to successive discounts of:
(i) 80% and 80%
(ii) 60% and 60%
(iii) 60% and 80%
Solution
(i) Successive discounts = 80% and 80%
Let M.P. = ₹100
Then S.P. after two discounts = ₹{100 (100 – 80)(100 – 80)/(100 × 100)
= (100 × 20 × 20)/(100 × 100)
= ₹4
∴ Total discounts = ₹ 100 – 4 = ₹96
∴ Single discount = 96%
(ii) Successive discounts = 60% and 60%
Let M.P. = ₹100
Then S.P. after two discounts, = {100(100 – 60)(100 – 60)/(100 × 100)
= (100 × 40 × 40)/(100 × 100)
= ₹16
∴ Total discount = ₹ 100 – 16 = ₹84
Single discount = 84 %
(iii) Successive discounts = 60% and 80%
let M.P. = ₹ 100
∴ S.P. after two discounts = ₹{100(100 - 60)(100 - 80)/(100 × 100)
= ₹(100 × 40 × 20)/(100 × 100)
= ₹ 8
∴ Total discount = ₹ 100 – 8 = ₹92
∴ Single discount = 92%
Exercise 8 E
1. Rajat purchases a wrist-watch costing Rs. 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.
Solution
Cost of watch = ₹540
Rate of Sales Tax = 8%
∴ Amount of Sales Tax = ₹540 × 8/100
= ₹4320/100
= ₹43.20
Total Amount of Watch = ₹540 + ₹43.20
= ₹ 583.20
2. Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution
On ₹3840, sales-tax is = ₹345.60
∴ Percent of Sales Tax = (345.60 × 100)/3840
= (34560 × 100)/(100 × 3840)
= 9%
3. The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.
Solution
Selling price of Washing machine = ₹13,530
Rate of Sales Tax = 10%
∴ Cost Price = (Selling Price × 100)/(100 + Rate of Sales Tax)
= (13530 × 100)/(100 + 10)
= (13530 × 100)/110
= ₹12,300
4. Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution
Cost of biscuits = ₹158
Sales Tax @ 6% = ₹158 × 6/100
= 948/100
= ₹9.48
Total price of biscuits = ₹158 + ₹9.48
= ₹167.48
Cost of cosmetic-goods = ₹354
Sales Tax @9% = ₹354 × 9/100
= 3186/100
= ₹31.86
Total Cost of cosmetic goods = ₹354 + ₹31.86 = ₹385.86
Total amount paid by Sarita = 167.48 + 385.86 = ₹535.34
5. The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?
Solution
Sale price of T.V. set = ₹13,407
Rate of sales ttax = 9%
Let marked price of T.V. = x
Then sale price = x + (x × 9)/100
= (100x + 9x)/100
= 109x/100
∴ 109x/100 = ₹ 13,407
x = (13407 × 100)/109
= ₹ 12,300
∴ Marked Price = ₹12,300
In second case, Sales Tax = 13%
∴ Amount of sales Tax = ₹12,300 × 13/100
= ₹1,599
∴ Sale price = ₹12,300 + 1,599 = ₹ 13,899
Difference between the two sales price = ₹13,899 - ₹ 13,407
= ₹ 492
6. The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution
Price of an article = ₹ 8,250
Rate of Sales Tax = 10%
Let the list price = x
∴ Sales tax = x × 10/100 = x/10
Sales price = x + x/10 = 11x/10
∴ 11x/10 = 8250
x = (8250 × 10)/11 = 7,500
∴ List price = ₹7,500
(i) Rate of sales tax = 15%
∴ Sale Price = ₹ 7,500 (100 + 15)100
= ₹7,500 × 115/100
= ₹ 8,625
∴ Customer will pay more.
Hence increase = 8,625 – 8,250 = ₹375
∴ Sale Price = ₹7,500 × (100 + 12)/100
= ₹ 7,500 × 107/100 = ₹ 8,025
∴ The customer will have to pay less = ₹8,250 - ₹ 8,025
= ₹ 225
7. A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution
8. When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution
Rate of sales tax in the beginning = 9%
And Reduced rate = 6%
∴ Diff. = 9 – 6 = 3%
Total saving = ₹ 780
∴ List price of TV = Total saving × 100/3
= (780 × 100)/3
= ₹26000
9. A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.
Solution
Sale Price of an article including S.T. = ₹ 21384
Rate of Sales Tax = 10%
∴ Actual price = (Total price × 100)/(100 + ST%)
= (21384 × 100)/(100 + 10)
= (21384 × 100)/110
= ₹ 19440
In the second case, rate of sales tax = 8%
∴ S.P. = ₹{19440 ×(100 + 8)/100}
= ₹(19440 × 108)/100
= ₹ 2099520/100
= ₹20995.20
∴ Extra profit = ₹21384 - ₹ 20995.20
= ₹388.80
Solution
Cost of watch = ₹540
Rate of Sales Tax = 8%
∴ Amount of Sales Tax = ₹540 × 8/100
= ₹4320/100
= ₹43.20
Total Amount of Watch = ₹540 + ₹43.20
= ₹ 583.20
2. Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution
On ₹3840, sales-tax is = ₹345.60
∴ Percent of Sales Tax = (345.60 × 100)/3840
= (34560 × 100)/(100 × 3840)
= 9%
3. The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.
Solution
Selling price of Washing machine = ₹13,530
Rate of Sales Tax = 10%
∴ Cost Price = (Selling Price × 100)/(100 + Rate of Sales Tax)
= (13530 × 100)/(100 + 10)
= (13530 × 100)/110
= ₹12,300
4. Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution
Cost of biscuits = ₹158
Sales Tax @ 6% = ₹158 × 6/100
= 948/100
= ₹9.48
Total price of biscuits = ₹158 + ₹9.48
= ₹167.48
Cost of cosmetic-goods = ₹354
Sales Tax @9% = ₹354 × 9/100
= 3186/100
= ₹31.86
Total Cost of cosmetic goods = ₹354 + ₹31.86 = ₹385.86
Total amount paid by Sarita = 167.48 + 385.86 = ₹535.34
5. The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?
Solution
Sale price of T.V. set = ₹13,407
Rate of sales ttax = 9%
Let marked price of T.V. = x
Then sale price = x + (x × 9)/100
= (100x + 9x)/100
= 109x/100
∴ 109x/100 = ₹ 13,407
x = (13407 × 100)/109
= ₹ 12,300
∴ Marked Price = ₹12,300
In second case, Sales Tax = 13%
∴ Amount of sales Tax = ₹12,300 × 13/100
= ₹1,599
∴ Sale price = ₹12,300 + 1,599 = ₹ 13,899
Difference between the two sales price = ₹13,899 - ₹ 13,407
= ₹ 492
6. The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution
Price of an article = ₹ 8,250
Rate of Sales Tax = 10%
Let the list price = x
∴ Sales tax = x × 10/100 = x/10
Sales price = x + x/10 = 11x/10
∴ 11x/10 = 8250
x = (8250 × 10)/11 = 7,500
∴ List price = ₹7,500
(i) Rate of sales tax = 15%
∴ Sale Price = ₹ 7,500 (100 + 15)100
= ₹7,500 × 115/100
= ₹ 8,625
∴ Customer will pay more.
Hence increase = 8,625 – 8,250 = ₹375
∴ Sale Price = ₹7,500 × (100 + 12)/100
= ₹ 7,500 × 107/100 = ₹ 8,025
∴ The customer will have to pay less = ₹8,250 - ₹ 8,025
= ₹ 225
7. A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution
8. When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution
Rate of sales tax in the beginning = 9%
And Reduced rate = 6%
∴ Diff. = 9 – 6 = 3%
Total saving = ₹ 780
∴ List price of TV = Total saving × 100/3
= (780 × 100)/3
= ₹26000
9. A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.
Solution
Sale Price of an article including S.T. = ₹ 21384
Rate of Sales Tax = 10%
∴ Actual price = (Total price × 100)/(100 + ST%)
= (21384 × 100)/(100 + 10)
= (21384 × 100)/110
= ₹ 19440
In the second case, rate of sales tax = 8%
∴ S.P. = ₹{19440 ×(100 + 8)/100}
= ₹(19440 × 108)/100
= ₹ 2099520/100
= ₹20995.20
∴ Extra profit = ₹21384 - ₹ 20995.20
= ₹388.80
Exercise 8 F
1. A shopkeeper buys an article for ₹ 8,000 and sells it for ₹ 10,000. If the rate of tax under VAT is 10%, find :
(i) tax paid by the shopkeeper
(ii) tax charged by the shopkeeper
(iii) VAT paid by the shopkeeper
Solution
Cost Price of an article = ₹8000
And, selling price = ₹10,000
(i) Tax paid by Shopkeeper under VAT 10% = ₹(8,000 × 10)/100
= ₹800
(ii) Tax charged by the shopkeeper
∵ Selling price = ₹10,000 under VAT 10%
= ₹(10,000 × 10)/100
= ₹1000
(iii) VAT paid by the shopkeeper = ₹1000 - ₹800 = ₹200
2. A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?
Solution
Cost price of goods = ₹12,000
VAT charged, under VAT 12% = (12,000 × 12)/100
= ₹1440
Selling price of goods = ₹15,000
VAT charged, Under VAT 12% = (15,000 × 12)/100
= ₹1800
VAT paid by trader = ₹1800 - ₹1400
= ₹360
3. The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.
Solution
M.P. of an article = ₹7000
Discount rate = 20%
C.P. for Manoj = ₹7000 – 20% of ₹7000
= ₹7000 - ₹1400
= ₹5600
∴ Tax paid for Manoj = ₹(5600 × 10)/100
= ₹560
S.P. of an article = ₹7000
Tax charged by Manoj = ₹(7000 × 10)/100
= ₹700
VAT paid = Tax charged – Tax paid
= ₹700 - ₹560
= ₹140
(i) tax paid by the shopkeeper
(ii) tax charged by the shopkeeper
(iii) VAT paid by the shopkeeper
Solution
Cost Price of an article = ₹8000
And, selling price = ₹10,000
(i) Tax paid by Shopkeeper under VAT 10% = ₹(8,000 × 10)/100
= ₹800
(ii) Tax charged by the shopkeeper
∵ Selling price = ₹10,000 under VAT 10%
= ₹(10,000 × 10)/100
= ₹1000
(iii) VAT paid by the shopkeeper = ₹1000 - ₹800 = ₹200
2. A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?
Solution
Cost price of goods = ₹12,000
VAT charged, under VAT 12% = (12,000 × 12)/100
= ₹1440
Selling price of goods = ₹15,000
VAT charged, Under VAT 12% = (15,000 × 12)/100
= ₹1800
VAT paid by trader = ₹1800 - ₹1400
= ₹360
3. The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.
Solution
M.P. of an article = ₹7000
Discount rate = 20%
C.P. for Manoj = ₹7000 – 20% of ₹7000
= ₹7000 - ₹1400
= ₹5600
∴ Tax paid for Manoj = ₹(5600 × 10)/100
= ₹560
S.P. of an article = ₹7000
Tax charged by Manoj = ₹(7000 × 10)/100
= ₹700
VAT paid = Tax charged – Tax paid
= ₹700 - ₹560
= ₹140
4. A buys some goods for ₹ 4,000 and sold them to B for ₹ 5,000. B sold these goods to C for ₹ 6,000. If the rate of tax (under VAT) at each stage is 5%, find :
(i) VAT paid by A
(ii) VAT paid by B
Solution
C.P. of some goods for A = ₹ 4000
C.P. of some goods for B = ₹ 5000
and C.P. for C = ₹ 6000
Rate of VAT in each case = 5%
∴ VAT charged by A = ₹4000 × 5/100 = ₹200
VAT charged by B = ₹5,000 × 5/100 = ₹250
VAT charged by C = ₹6000 × 5/100 = ₹300
(i) Now VAT paid by A = ₹250 - ₹200 = ₹50
(ii) Now VAT paid by B = ₹300 - ₹250 = ₹50
5.A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :
(i) tax paid by A
(ii) tax charged by A
(iii) VAT paid by A
Solution
6. A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.
Solution
C.P. of article = ₹ 12,400
Rate of VAT = 8%
Total VAT = ₹ 12,400 × 8/100 = ₹ 992
S.P. of the article = ₹ 17000
VAT charge 8% = ₹ 17000 × 8/100 = ₹ 1360
Amount of VAT paid by the shopkeeper = ₹ 1360 – ₹ 992 = ₹ 368
7. A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.
Solution
C.P. of an article for A = ₹ 7,200
C.P. of the article for B = ₹9600
And C.P. for C = ₹11000
Rate of VAT in each case = 10%
∴ VAT charged by A = ₹7200 × 10/100 = ₹ 720
VAT charged by B = ₹9600 × 10/100 = ₹960
And VAT charged by C = ₹11000 × 10/100
= ₹1100
Now VAT levied on A = ₹960 - ₹720
= ₹240
And VAT levied on B = ₹1100 - ₹960
= ₹140
8. A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.
Solution
C.P. of raw material = ₹60000
Rate of tax = 5%
∴ Total tax = ₹60000 × 5/100 = ₹3000
S.P. of that material = ₹80,000
Rate of tax = 12%
∴ Total tax = ₹80,000 × 12/100 = ₹ 9600
VAT paid by manufacturer = ₹ 9600 - ₹3000 = 6600
9. The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:
(i) distributor
(ii) trader
Solution
Cost price of an article to a distributor = ₹6000
And selling price of distributor = ₹7500
And selling price of trader = ₹8000
Rate of VAT = 12.5% = 25/2%
Now, VAT for two distributor = ₹(6000 × 25)/(100 × 2)
= ₹750
And VAT for two trader = (7500 × 25)/(100 × 2)
= ₹937.50
And VAP for customer = (8000 × 25)/(100 × 2)
= ₹1000
(i) Now VAT paid by distributor = ₹937.50 - ₹750
= ₹ 187.50
(ii) and VAT paid by trader = ₹1000 - ₹937.50 = ₹62.50
10. The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.
Solution
M.P. of an article = ₹10,000
A purchased it at discount of = 30%
C.P. of an article = M.P. – (Discount rate × M.P.)/100
= ₹10,000 – (30 × 10,000)/100
= ₹10,000 - ₹3000
= ₹7000
Tax rate = 5%
Tax paid by A = C.P. × Tax rate/100
= ₹7000 × 5/100
= ₹350
Now, A sold the article at 10% discount
∴ S.P. of an article = M.P. – (Discount rate × M.P.)/100
= ₹10,000 – (10 × ₹10,000)/100
= ₹10,000 - ₹1000 = ₹9000
Tax charged by A = S.P. × Tax rate/100
= ₹9000 × 5/100 = ₹450
∴ VAT paid by A = Tax charged – Tax paid
= ₹450 - ₹ 350
= ₹100
(i) VAT paid by A
(ii) VAT paid by B
Solution
C.P. of some goods for A = ₹ 4000
C.P. of some goods for B = ₹ 5000
and C.P. for C = ₹ 6000
Rate of VAT in each case = 5%
∴ VAT charged by A = ₹4000 × 5/100 = ₹200
VAT charged by B = ₹5,000 × 5/100 = ₹250
VAT charged by C = ₹6000 × 5/100 = ₹300
(i) Now VAT paid by A = ₹250 - ₹200 = ₹50
(ii) Now VAT paid by B = ₹300 - ₹250 = ₹50
5.A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :
(i) tax paid by A
(ii) tax charged by A
(iii) VAT paid by A
Solution
6. A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.
Solution
C.P. of article = ₹ 12,400
Rate of VAT = 8%
Total VAT = ₹ 12,400 × 8/100 = ₹ 992
S.P. of the article = ₹ 17000
VAT charge 8% = ₹ 17000 × 8/100 = ₹ 1360
Amount of VAT paid by the shopkeeper = ₹ 1360 – ₹ 992 = ₹ 368
7. A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.
Solution
C.P. of an article for A = ₹ 7,200
C.P. of the article for B = ₹9600
And C.P. for C = ₹11000
Rate of VAT in each case = 10%
∴ VAT charged by A = ₹7200 × 10/100 = ₹ 720
VAT charged by B = ₹9600 × 10/100 = ₹960
And VAT charged by C = ₹11000 × 10/100
= ₹1100
Now VAT levied on A = ₹960 - ₹720
= ₹240
And VAT levied on B = ₹1100 - ₹960
= ₹140
8. A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.
Solution
C.P. of raw material = ₹60000
Rate of tax = 5%
∴ Total tax = ₹60000 × 5/100 = ₹3000
S.P. of that material = ₹80,000
Rate of tax = 12%
∴ Total tax = ₹80,000 × 12/100 = ₹ 9600
VAT paid by manufacturer = ₹ 9600 - ₹3000 = 6600
9. The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:
(i) distributor
(ii) trader
Solution
Cost price of an article to a distributor = ₹6000
And selling price of distributor = ₹7500
And selling price of trader = ₹8000
Rate of VAT = 12.5% = 25/2%
Now, VAT for two distributor = ₹(6000 × 25)/(100 × 2)
= ₹750
And VAT for two trader = (7500 × 25)/(100 × 2)
= ₹937.50
And VAP for customer = (8000 × 25)/(100 × 2)
= ₹1000
(i) Now VAT paid by distributor = ₹937.50 - ₹750
= ₹ 187.50
(ii) and VAT paid by trader = ₹1000 - ₹937.50 = ₹62.50
10. The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.
Solution
M.P. of an article = ₹10,000
A purchased it at discount of = 30%
C.P. of an article = M.P. – (Discount rate × M.P.)/100
= ₹10,000 – (30 × 10,000)/100
= ₹10,000 - ₹3000
= ₹7000
Tax rate = 5%
Tax paid by A = C.P. × Tax rate/100
= ₹7000 × 5/100
= ₹350
Now, A sold the article at 10% discount
∴ S.P. of an article = M.P. – (Discount rate × M.P.)/100
= ₹10,000 – (10 × ₹10,000)/100
= ₹10,000 - ₹1000 = ₹9000
Tax charged by A = S.P. × Tax rate/100
= ₹9000 × 5/100 = ₹450
∴ VAT paid by A = Tax charged – Tax paid
= ₹450 - ₹ 350
= ₹100