Selina Concise Solutions for Chapter 9 Profit, Loss and Discount Class 7 ICSE Mathematics

Exercise 9 (A)


1. Find the gain or loss percent, if
(i) C.P. = Rs. 200 and S.P.: = Rs. 224
(ii) C.P. = Rs. 450 and S.P. = Rs. 400
(iii) C.P. = Rs. 550 and gain = Rs. 22
(iv) CP. = Rs. 216 and loss = Rs. 72
(v) S.P. = Rs. 500 and loss : = Rs. 100
(vi) S.P. = Rs. 12 and profit = Rs. 4
(vii) C.P. = Rs. 5 and gain = 60 P

Answer 

(i) C.P. = Rs. 200 and S.P. = Rs. 224
∴ Gain = S.P. - C.P. 
= Rs. 224 - Rs. 200 = Rs. 24 


2. Find the selling price, if:
(i) C.P. = Rs. 500 and gain = 25%
(ii) C.P. = Rs. 60 and loss = 12 1/2%
(iii) C.P. = Rs. 150 and loss = 20%
(iv) C.P. = Rs. 80 and gain = 2.5%
Answer 

3. Rohit bought a tape-recorder for Rs. 1,500 and sold it for Rs. 1,800. Calculate his profit or loss percent.
Answer 
C.P. of tape - recorder = Rs. 1500 
S.P. = Rs. 1800
∴ Gain = S.P. - C.P. 
= Rs. 1800 - Rs. 1500 = Rs. 300 

4. An article bought for Rs. 350 is sold at a profit of 20% . Find its selling price. 
Answer 
C.P. of article = Rs. 350 
Profit = 20% 

5. An old machine is bought for Rs. 1,400 and is sold at a loss of 15 %. Find its selling price. 
Answer 
C.P. of the machine = Rs. 1400 
Loss = 15%

6. Oranges are bought at 5 for Rs. 10 and sold at 6 for Rs. 15. Find profit or loss as percent. 
Answer 
L.C.M.  of 5 and 6 = 30 
Let 30 oranges are bought 
∴ C.P. of 30 oranges = (30×10)/5 = Rs. 60 
and S.P. of 30 oranges = (30×15)/6 = Rs. 75 
Gain = S.P. - C.P. = Rs. 75 - Rs. 60 = Rs. 15 

7.  A certain number of articles are bought at 3 for Rs. 150 and all of them are sold at 4 for Rs. 180. Find the loss or gain as percent.
Answer 
L.C.M of 3 and 4 = 12 
Let 12 articles are bought 
∴ C.P. of 12 articles = Rs. (150×12)/3 = Rs. 600 
and S.P. of 12 articles = Rs. (180×12)/4 = Rs. 540 
Loss = C.P. - S.P. 
= Rs. 600 - Rs. 540 = Rs. 60

8. A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.
Answer 
Quantity of sweets bought = 120 
∴ C.P. of 120 sweets = (12020)/100 = Rs. 24 
No. of sweets consumed = 18 
Balance sweets = 120 - 18 = 102 
∴ S.P.  of 102 sweets 

9. The cost price of an article is Rs. 1,200 and selling price is times of its cost price. Find:
(i) selling price of the article
(ii) profit or loss as percent.
Answer
Cost price (C.P.) = Rs. 1200
∴ S.P. = 5/4 of C.P.
= (5/4)× 1200 = Rs. 1500
∴ Gain = S.P. - C.P. 
= Rs. 1500 - Rs. 1200 = Rs. 300

10. The selling price of an article is Rs. 1,200 and cost price is times of its selling price, find :
(i) cost price of the article ;
(ii) profit or loss as percent.
Answer 
(i) S.P. of an article = Rs. 1200
∴ C.P. = (5/4) of S.P. = (5/4)× 1200 = Rs. 1500
(ii) Loss = C.P. - S.P. 
= Rs. 1500 - Rs. 1200 = Rs. 300

Exercise 9 (B)


1. Find the cost price, if:
(i) S.P. = Rs. 21 and gain = 5%
(ii) S.P. = Rs. 22 and loss = 12%
(iii) S.P. = Rs. 340 and gain = Rs. 20
(iv) S.P. = Rs. 200 and loss = Rs. 50
(v) S.P. = Re. 1 and loss = 5 p.
Answer 

(iii) S.P. = Rs. 340, Gain = Rs. 20 
∴ C.P. = S.P. - Gain
= Rs. 340 - Rs. 20 = Rs. 320

(iv) S.P. = Rs. 200
Loss = Rs. 50 
∴ C.P. = S.P. + loss 
= Rs. 200 + Rs. 50 = Rs. 250 

(v) S.P.  = Re 1, Loss = 5 paise
∴ C.P. = S.P. + loss 
= Re 1 + 5 P
= Rs. 1.05

2. By selling an article for Rs. 810, a loss of 10 percent is suffered. Find its cost price.
Answer 
S.P. of an article = Rs. 810 
Loss = 10% 

3. By selling a scooter for Rs. 9,200, a man gains 15%. Find the cost price of the scooter. 
Answer 
S.P. of the scooter = Rs. 9200
Gain = 15% 

4. On selling an article for Rs. 2,640, a profit of 10 percent is made. Find
(i) cost price of the article
(ii) new selling price of it, in order to gain 15%
Answer 
S.P. of an article = Rs. 2640 
Gain = 10% 

5.  A T.V. set is sold for Rs. 6800 at a loss of 15%. Find
(i) cost price of the T.V. set.
(ii) new selling price of it, in order to gain 12%
Answer 
S.P.  of the T.V. set = Rs. 6800
Loss = 15% 

6. A fruit seller bought mangoes at Rs. 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for.
(i) one mango
(ii) 40 mangoes 
Answer 
C.P. of 1 dozen or 12 mangoes = Rs. 90 
Loss = 8% 
∴ S.P. of 1 dozen or 12 mangoes 

(i) S.P. of 1 mango = 82.80/12 = Rs. 6.90 
(ii) S.P. of 40 mangoes = Rs. 6.90×40 = Rs. 276 

7. By selling two transistors for Rs. 00 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other.
Find :
(i) C.P. of each transistor
(ii) total C.P. and total S.P. of both the transistors
(iii) profit or loss percent on the whole.
Answer 
S.P. of first transistor = Rs. 600
Gain = 20% 

∴ C.P. of the two transistors are Rs. 500 and Rs. 750

(ii) Total C.P. of both  the transistors 
= Rs. 500 + Rs. 750 = Rs. 1250
and total S.P. of both the transistors 
= Rs. 600 + Rs. 600 = Rs. 1200

(iii) Total loss = C.P. - S.P. 
= 1250 - 1200 = Rs. 50 

8. Mangoes are bought at 20 for Rs. 60. If they are sold atpercent profit. Find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Answer 
C.P. of 20 mangoes = Rs. 60 
Gain == 100/3 % 
(i) S.P. of 1 mango = Rs.  80/20 = Rs. 4 
(ii) S.P. of 8 mangoes = Rs. 4× 8 = Rs. 32 

9. Find the cost price of an article, which is sold for Rs. 4050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Answer 
S.P. of an article = Rs. 4050
Loss = 10% 

10. By selling an article for ₹825, a man loses equal to j of its selling price. Find :
(i) the cost price of the article,
(ii) the profit percent or the loss percent made, if the same article is sold for ₹1265.
Answer 
S.P. of an article = ₹ 825
Loss = 1/3 of S.P. = (1/3)× 825 = ₹ 275 
(i) ∴ C.P. = S.P. + Loss 
= ₹ 825 + ₹ 275 = ₹ 1100 
(ii) In second case, 
S.P. = ₹ 1265 
∴ Gain = S.P. - C.P. 
= ₹ 1265 - ₹ 1100 = ₹ 165 

11. Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles. 
Answer 
C.P. of 10 articles = S.P. of 8 articles = ₹ 80 (suppose)
∴ C.P. of 1 article = 80/10 = ₹8 
and S.P. of  1 article = 80/8 = ₹ 10 
∴ Gain = S.P. - C.P. = ₹ 10 - ₹ 8 = ₹ 2

12.  Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.
Answer 
C.P. of 8 articles = S.P. of 10 articles = ₹ 80  (suppose)
∴ C.P. of 1article = 80/8 = ₹ 10 
and S.P. of 1 article = 80/10 = ₹ 8 
∴ Loss = C.P. - S.P. = ₹ 10 - ₹ 8 = ₹ 2

13. The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Answer 
Let S.P. = ₹ 100
C.P. = 96% of S.P. 
= ₹ (96/100)×100 = ₹96
∴ Gain  = ₹ 100 - ₹ 96 = ₹ 4
and, Gain percent 

14. The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole. 
Answer 
Let C.P. = ₹ 100
S.P. = 96% of C.P. 
= ₹ (96/100)× 100 = ₹ 96
∴ Loss = ₹ 100 - ₹ 96 = ₹ 4 

15. Hundred oranges are bought for ₹350 and all of them are sold at the rate of ₹48 per dozen. Find the profit percent or loss percent made. 
Answer 
∵ C.P.  of one orange = ₹(350/100)  = ₹3.50
and S. P. of one orange = ₹(48/12) = ₹ 4
Clearly, Gain = ₹ 4 - ₹ 3.50 = ₹0.50
and Gain percent = (Gain ×100)/C.P. = ₹ (0.50/3.50)× 100%
=

16. Oranges are bought at 100 for ?80 and all of them are sold at ₹80 for ₹100. Find the loss or gain as percent in this transaction.
Answer 
∵ C.P. of one orange = ₹ 80/100 = ₹ 0.8 
and S.P. of one orange = ₹ 100/80 = ₹ 1.25 
Clearly, profit = ₹ 1.25 - ₹ 0.8 = ₹ 0.45

17. An article is bought for ₹5,700 and ₹1,300 is spent on its repairing, transportation, etc. For how much should this article be sold in order to gain 20% on the whole.
Answer
C.P. of an article = ₹ 5700
Amount spent on repair = ₹ 1300
Total cost price(C.P.) = ₹ 5700 + ₹ 1300 = ₹ 7000
Gain = 20% 


Exercise 9 (C)


1. A machine is marked at ₹5000 and is sold at a discount of 10%. Find the selling price of the machine.
Answer 
Marked price (M.P.) of the machine = ₹ 5000
Rate of discount = 10% 
∴ Amount of discount = ₹ 5000 × (10/100) = ₹ 500
∴ Selling price = M.P. - discount 
= ₹5000 - ₹ 500 = ₹ 4500

2. shopkeeper marked a dinner set for ₹1000. He sold it at ₹900, what percent discount did he give ?
Answer 
Marked price of a dinner set = ₹ 1000
and selling price (S.P.) = ₹ 900
∴ Amount of discount = Rs. 1000 - ₹ 900 = ₹ 100

3. A pair of shoes marked at ₹320, are sold at a discount of 15 percent.
Find :
(i) discount
(ii) selling price of the shoes. 
Answer
Marked Price(M.P.) of shoes = ₹ 320 
Rate of discount = 15% 
(i) ∴ Amount of discount = ₹ (320×15)/100 = ₹ 48
(ii) Selling price = M.P. - Discount 
= ₹ 320 - 48 = ₹ 272

4. The list price of an article is ₹450 and it is sold for ₹360.
Find :
(i) discount
(ii) discount percent
Answer 
List price(M.P.) of an article = ₹ 450
Selling price = ₹ 360 
(i) ∴ Amount of discount = M.P. - S.P. 
= ₹ 450 - ₹ 360 = ₹ 90 

5. A shopkeeper buys an article for ₹300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Answer 
C.P. of an article = ₹ 300
Increase in price = 20% 
(i) ∴ Marked price (M.P.) 

6. A car is marked at Rs. 50,000. The dealer gives 5% discount on first Rs. 20,000 and 2% discount on the remaining Rs. 30,000.
Find :
(i) the total discount.
(ii) the price charged by the dealer.
Answer 
Marked Price (M.P.) of a car = Rs. 50,000
Discount at the rate of 5% on first 
Rs. 20,000 = Rs. (20,000×5)/100 = Rs. 1000
Discount at the rate of 2% on remaining 
Rs. 30,000 = Rs. (30,000× 2)/100 = Rs. 600
(i) ∴ Total discount = Rs. 1000 + Rs. 600 = Rs. 1600
(ii) Price charged by the dealer 
= Rs. 50000  - Rs. 1600 = Rs. 48400

7. A dealer buys a T.V. set for Rs. 2500. He marks it at Rs. 3,200 and then gives a discount of 10% on it.
Find :
(i) the selling price of the T.V. set
(ii) the profit percent made by the dealer.
Answer 
C.P. of a T.V. set = Rs. 2500, M.P. = Rs. 3,200
Rate of discount = 10% 

8. A sells his goods at 15% discount. Find the price of an article which is sold for Rs. 680.
Answer 
S.P.  of an article = Rs. 680 
Rate of discount = 15% 
Let M.P. of the article = Rs. 100 
∴ S.P. = Rs. 100 - 15 = Rs. 85 
If S.P. is Rs. 85, then M.P. = Rs. 100
and if S.P. is Rs. 680, then M.P. 
= Rs. (100×680)/85 = Rs. 800

9. A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges Rs. 560.
Answer 
Let Marked Price (M.P.) = Rs. 100
Discount = 20% 
∴ S.P. of that article = Rs. 100 - 20 = Rs. 80 . 
If S.P. is Rs. 80, then marked price = Rs. 100
and if S.P. is Rs. 560, then marked price 

10. An article is bought for Rs. 1,200 and Rs. 100 is spent on its transportation, etc. Find :
(i) the total C.P. of the article.
(ii) the selling price of it in order to gain 20% on the whole. 
Answer 
C.P. of an article = Rs. 1200 
Amount spent on transportation =Rs. 100
(i) Total C.P. of that article = Rs. 1200+ 100 = Rs. 1300

11. 40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 80. Find :
(i) C.P. of one pen.
(ii) S/P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens. Are the results of parts (iv) and (viii) same? What conclusion do you draw from the above result ?
Answer 

(v) C.P. of 40 pens = 40×12.50 = Rs. 500
(vi) S.P. of 40 pens = 40×16 = Rs. 640 
(vii) Profit on 40 pens = S.P. - C.P.
= Rs. 640 - 500
= Rs. 140 

= 28% 
Yes, the results of (iv) and (viii) are same. 
We see that profit of on equal number  of articles remains the same . 

12.  The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought are sold.
Answer 
C.P. of 5 articles = S.P. of  4 articles 
Let C.P. of 5 articles = S.P. of 4 articles = Rs. 100
∴ C.P. of 1 articles = Rs. 100/5 = Rs. 20
and S.P. of 1 article = Rs. 100/4 = Rs. 25 
∴ Profit = S.P.  - C.P. = Rs. 25 - Rs. 20 = Rs. 5 

13. The C.P. of 8 pens is same as S.P. of 10 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold 
Answer 
C.P. of 8 pens = S.P.  of 10 Pens = Rs. 100 (suppose) 
∴ C.P. of 1 pen = 100/8 = Rs. 12.50
and S.P.  of 1 pen = 100/10 = Rs. 10 
∴ Loss = C.P. - S.P. = Rs. 12.50 - Rs. 10 = Rs. 2.50 

14. A certain number of articles are bought at Rs. 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:
(i) one article
(ii) seven articles. 
Answer 
C.P. of 1 dozen articles = Rs. 450 
Profit = 20% 

15. An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made. 
Answer 
Let cost price of an article = Rs. 100 
Marked price = Rs. 100 + 60 = Rs. 160 
Rate of discount = 20% 
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