# 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

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%

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%

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

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

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

∴ 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

∴ 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

∴ 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**

(iv) S.P. = Rs. 200

Loss = Rs. 50

∴ C.P. = S.P. + loss

= Rs. 200 + Rs. 50 = Rs. 250

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

∴ 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%

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%

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%

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%

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

Loss = 8%

∴ S.P. of 1 dozen or 12 mangoes

**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%

Gain = 20%

(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

= 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

= 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**

(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%

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

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

∴ 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

∴ 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

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

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%

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

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%

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

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

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 = ₹ 48Rate of discount = 15%

(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

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.)

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

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

= 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%

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

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

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

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

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

∴ 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%

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%

Marked price = Rs. 100 + 60 = Rs. 160

Rate of discount = 20%