Class 7: Maths Chapter 9 solutions. Complete Class 7 Maths Chapter 9 Notes.
Selina Class 7 ICSE Solutions Mathematics : Chapter 9- Profit, Loss and Discount
Selina 7th Maths Chapter 9, Class 7 Maths Chapter 9 solutions
Exercise 9A page: 104
1. Find the gain or loss percent, if:
(i) C.P. = ₹ 200 and S.P. = ₹ 224
(ii) C.P. = ₹ 450 and S.P. = ₹ 400
(iii) C.P. = ₹ 550 and gain = ₹ 22
(iv) C.P. = ₹ 216 and loss = ₹ 72
(v) S.P. = ₹ 500 and loss = ₹ 100
Solution:
(i) C.P. = ₹ 200 and S.P. = ₹ 224
We know that
Gain = S.P. – C.P.
So we get
= 224 – 200
= ₹ 24
So we get
Gain percent = (gain × 100)/ C.P.
Substituting the values
= (24 × 100)/ 200
= 12%
(ii) C.P. = ₹ 450 and S.P. = ₹ 400
We know that
Loss = C.P. – S.P.
So we get
= 450 – 400
= ₹ 50
So we get
Loss percent = (loss × 100)/ C.P.
Substituting the values
= (50 × 100)/ 450
= 100/9
= 11 1/9%
(iii) C.P. = ₹ 550 and gain = ₹ 22
We know that
S.P. = C.P. + gain
So we get
= 550 + 22
= ₹ 572
So we get
Gain percent = (gain × 200)/ C.P.
Substituting the values
= (22 × 100)/ 550
= 4%
(iv) C.P. = ₹ 216 and loss = ₹ 72
We know that
S.P. = C.P. – loss
So we get
= 216 – 72
= ₹ 144
So we get
Loss percent = (loss × 100)/ C.P.
Substituting the values
= (72 × 100)/ 216
= 100/3
= 33 1/3%
(v) S.P. = ₹ 500 and loss = ₹ 100
We know that
C.P. = S.P. + loss
So we get
= 500 + 100
= ₹ 600
So we get
Loss percent = (loss × 100)/ C.P.
Substituting the values
= (100 × 100)/ 600
= 50/3
= 16 2/3 %
2. Find the selling price, if:
(i) C.P = ₹ 500 and gain = 25%
(ii) C.P. = ₹ 60 and loss = 12 ½ %
Solution:
(i) C.P = ₹ 500 and gain = 25%
We know that
S.P. = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [500 (100 + 25)]/ 100
We get
= (500 × 125)/ 100
= ₹ 625
(ii) C.P. = ₹ 60 and loss = 12 ½ %
We know that
Loss = 12 ½ % = 25/2%
Here
S.P. = [C.P. (100 – Loss percent)]/ 100
Substituting the values
= [60 (100 – 25/2)]/ 100
So we get
= [60 (200 – 25/ 2)]/ 100
We can write it as
= (60 × 175)/ (2 × 100)
= ₹ 105/2
= ₹ 52.50
3. Rohit bought a tape-recorder for ₹ 1,500 and sold it for ₹ 1,800. Calculate his profit or loss percent.
Solution:
It is given that
C.P of tape-recorder = ₹ 1,500
S.P of tape-recorder = ₹ 1,800
We know that
Gain = S.P – C. P
= 1800 – 1500
= ₹ 300
Gain percent = (Gain × 100)/ C.P
Substituting the values
= (300 × 100)/ 1500
= 20%
4. An article bought for ₹ 350 is sold at a profit of 20%. Find its selling price.
Solution:
It is given that
C.P of an article = ₹ 350
Profit = 20%
We know that
S.P = [C.P (100 + profit percent)]/ 100
Substituting the values
= [350 (100 + 20)]/ 100
So we get
= (350 × 120)/ 100
= ₹ 420
5. An old machine is bought for ₹ 1,400 and is sold at a loss of 15%. Find its selling price.
Solution:
It is given that
C.P. of the old machine = ₹ 1,400
Loss percent = 15%
We know that
S.P = [C.P (100 – loss percent)]/ 100
Substituting the values
= [1400 (100 – 15)]/ 100
By further calculation
= (1400 × 85)/ 100
= ₹ 1190
6. Oranges are bought at 5 for ₹ 10 and sold at 6 for ₹ 15. Find profit or loss as percent.
Solution:
We know that
LCM of 5 and 6 = 30
Consider that 30 oranges are bought
So the C.P of 30 oranges = (30 × 10)/ 5 = ₹ 60
S.P of 30 oranges = (30 × 15)/ 6 = ₹ 75
Gain = S.P – C.P
Substituting the values
= 75 – 60
= ₹ 15
Gain percent = (gain × 100)/ C.P
Substituting the values
= (15 × 100)/ 60
= 25%
7. A certain number of articles are bought at 3 for ₹ 150 and all of them are sold at 4 for ₹ 180. Find the loss or gain as percent.
Solution:
We know that
LCM of 3 and 4 = 12
Consider that 12 articles are bought
So the C.P of 12 articles = (150 × 12)/ 3 = ₹ 600
S.P of 12 articles = (180 × 12)/ 4 = ₹ 540
Loss = C.P – S.P
Substituting the values
= 600 – 540
= ₹ 60
Loss percent = (loss × 100)/ C.P
Substituting the values
= (60 × 100)/ 600
= 10%
8. A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30p each. Find his profit or loss as percent.
Solution:
No. of sweets bought = 120
C.P of 120 sweets = (120 × 20)/ 100 = ₹ 24
No. of sweets consumed = 18
So the balance sweets = 120 – 18 = 102
S.P of 102 sweets = (102 × 30)/ 100 = ₹ 30.60
Gain = S.P – C.P
Substituting the values
= 30.60 – 24
= ₹ 6.60
Gain percent = (gain × 100)/ C.P
Substituting the values
= (6.60 × 100)/ 24
Multiplying both numerator and denominator by 100
= (660 × 100)/ (100 × 24)
= 55/2
= 27.5%
9. The cost price of an article is ₹ 1,200 and selling price is 5/4 times of its cost price.
Find:
(i) Selling price of the article,
(ii) Profit or loss as percent.
Solution:
It is given that
C.P of an article = ₹ 1,200
We know that
S.P = 5/4 of C.P
Substituting the values
S.P = 5/4 × 1200 = ₹ 1,500
Gain = S.P – C.P
Substituting the values
= 1500 – 1200
= ₹ 300
Gain percent = (gain × 100)/ C.P
Substituting the values
= (300 × 100)/ 1200
= 25%
10. The selling price of an article is ₹ 1,200 and cost price is 5/4 times of its selling price.
Find:
(i) cost price of the article,
(ii) profit or loss as percent.
Solution:
(i) S.P of an article = ₹ 1,200
We know that
C.P = 5/4 of S.P
Substituting the values
= 5/4 × 1200
= ₹ 1,500
(ii) Loss = C.P – S.P
Substituting the values
= 1500 – 1200
= ₹ 300
Loss percent = (loss × 100)/ C.P
Substituting the values
= (300 × 100)/ 1500
So we get
= 100/5
= 20%
Exercise 9B page: 107
1. Find the cost price, if:
(i) S.P. = ₹ 21 and gain = 5%
(ii) S.P. = ₹ 22 and loss = 12%
(iii) S.P. = ₹ 340 and gain = ₹ 20
(iv) S.P. = ₹ 200 and loss = ₹ 50
(v) S.P. = ₹ 1 and loss = 5 p
Solution:
(i) S.P. = ₹ 21 and gain = 5%
We know that
C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (21 × 100)/ (100 + 5)
= (21 × 100)/ 105
So we get
= ₹ 20
(ii) S.P. = ₹ 22 and loss = 12%
We know that
C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (22 × 100)/ (100 – 12)
= (22 × 100)/ 88
So we get
= ₹ 25
(iii) S.P. = ₹ 340 and gain = ₹ 20
We know that
C.P. = S.P. – Gain
Substituting the values
= 340 – 20
= ₹ 320
(iv) S.P. = ₹ 200 and loss = ₹ 50
We know that
C.P. = S.P. + loss
Substituting the values
= 200 + 50
= ₹ 250
(v) S.P. = ₹ 1 and loss = 5 p
We know that
C.P. = S.P. + Loss
Substituting the values
= ₹ 1 + 5 p
= ₹ 1.05
2. By selling an article for ₹ 810, a loss of percent is suffered. Find its cost price.
Solution:
It is given that
S.P of an article = ₹ 810
Loss percent = 10 %
We know that
C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (810 × 100)/ (100 – 10)
So we get
= (810 × 100)/ 90
= ₹ 900
3. By selling a scooter for ₹ 9,200, a main gains 15%. Find the cost price of the scooter.
Solution:
It is given that
S.P. of the scooter = ₹ 9,200
Gain percent = 15%
We know that
C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (9200 × 100)/ (100 + 15)
= (9200 × 100)/ 115
So we get
= ₹ 8000
4. On selling an article for ₹ 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%.
Solution:
It is given that
S.P. of an article = ₹ 2,640
Gain percent = 10%
(i) C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (2640 × 100)/ (100 + 10)
= (2640 × 100)/ 110
So we get
= ₹ 2400
(ii) Gain percent = 15%
S.P. = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [2400 (100 + 15)]/ 100
So we get
= (2400 × 115)/ 100
= ₹ 2760
5. A T.V. set is sold for ₹ 6,800 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%.
Solution:
It is given that
S.P. of the T.V. set = ₹ 6,800
Loss percent = 15%
(i) C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (6800 × 100)/ (100 – 15)
So we get
= (6800 × 100)/ 85
= ₹ 8000
(ii) Gain percent = 12%
We know that
S.P. = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [8000 (100 + 12)]/ 100
So we get
= (8000 × 112)/ 100
= ₹ 8960
6. A fruit seller bought mangoes at ₹ 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
Solution:
It is given that
C.P. of 1 dozen mangoes = ₹ 90
Loss percent = 8%
Here the S.P of 1 dozen mangoes = [C.P. (100 – loss percent)]/ 100
Substituting the values
= [900 (100 – 8)]/ 100
So we get
= (90 × 92)/ 100
= ₹ 82.80
(i) S.P. of one mango = 82.80/12 = ₹ 6.90
(ii) S.P. of 40 mangoes = 6.90 × 40 = ₹ 276
7. By selling two transistors for ₹ 600 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.
Solution:
It is given that
S.P of first transistor = ₹ 600
Gain percent = 20%
(i) C.P = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (600 × 100)/ (100 + 20)
= (600 × 100)/ 120
So we get
= ₹ 500
S.P of the second transistor = ₹ 600
Loss percent = 20%
So the C.P of the other transistor = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (600 × 100)/ (100 – 20)
So we get
= (600 × 100)/ 80
= ₹ 750
Hence, C.P of the two transistors are ₹ 500 and ₹ 750.
(ii) Total C.P of both the transistors = 500 + 750 = ₹ 1250
Total S.P of both the transistors = 600 + 600 = ₹ 1200
(iii) We know that
Total loss = C.P – S.P
Substituting the values
= 1250 – 1200
= ₹ 50
So the loss percent = (loss × 100)/ C.P
Substituting the values
= (50 × 100)/ 1250
= 4%
8. Mangoes are bought at 20 for ₹ 60. If they are sold at a profit of 33 1/3 percent, find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Solution:
It is given that
C.P of 20 mangoes = ₹ 60
Gain percent = 33 1/3 % = 100/3 %
S.P of 20 mangoes = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [60 (100 + 100/3)]/ 100
So we get
= (60 × 400)/ (100 × 3)
= ₹ 80
(i) S.P of one mango = 80/20 = ₹ 4
(ii) S.P of 8 mangoes = 4 × 8 = ₹ 32
9. Find the cost price of an article, which is sold for ₹ 4,050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Solution:
It is given that
S.P of an article = ₹ 4,050
Loss percent = 10%
(i) C.P of the article = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (4050 × 100)/ (100 – 10)
So we get
= (4050 × 100)/ 90
= ₹ 4500
(ii) Gain percent = 8%
S.P of the article = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [4500 (100 + 8)]/ 100
So we get
= (4500 × 108)/ 100
= ₹ 4860
10. By selling an article for ₹ 825, a man losses an amount equal to 1/3 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 ₹ 1,265.
Solution:
It is given that
S.P of an article = ₹ 825
Loss = 1/3 of S.P = 1/3 × 825 = ₹ 275
(i) C.P = S.P + Loss
Substituting the values
= 825 + 275
= ₹ 1100
(ii) S.P = ₹ 1265
We know that
Gain = S.P – C.P
Substituting the values
= 1265 – 1100
= ₹ 165
Gain percent = (gain × 100)/ C.P
Substituting the values
= (165 × 100)/ 1100
= 15%
11. Find the loss or gain as percent, if the C.P. of articles, all of the same kind, is equal to S.P. of 8 articles.
Solution:
Consider C.P of 10 articles = S.P of 8 articles = ₹ 80
So the C.P of 1 article = 80/10 = ₹ 8
S.P of 1 article = 80/8 = ₹ 10
We know that
Gain = S.P – C.P
Substituting the values
= 10 – 8
= ₹ 2
Gain percent = (gain × 100)/ C.P
Substituting the values
= (2 × 100)/ 8
= 25%
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.
Solution:
Consider C.P of 8 articles = S.P of 10 articles = ₹ 80
So the C.P of 1 article = 80/8 = ₹ 10
S.P of 1 article = 80/10 = ₹ 8
We know that
Loss = C.P – S.P
Substituting the values
= 10 – 8
= ₹ 2
Loss percent = (loss × 100)/ C.P
Substituting the values
= (2 × 100)/ 10
= 20%
13. The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Solution:
Consider S.P = ₹ 100
We know that
C.P = 96% of S.P
So we get
= 96/100 × 100
= ₹ 96
Gain = 100 – 96 = ₹ 4
Gain percent = (gain × 100)/ C.P
Substituting the values
= 4/96 × 100%
= 25/6 or 4 1/6%
14. The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Solution:
Consider C.P = ₹ 100
S.P = 96% of C.P
So we get
= 96/100 × 100
= ₹ 96
Loss = 100 – 96 = ₹ 4
Loss percent = (loss × 100)/ C.P
Substituting the values
= 4/100 × 100%
= 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.
Solution:
It is given that
C.P of one orange = 350/100 = ₹ 3.50
S.P of one orange = 48/12 = ₹ 4
Gain = 4 – 3.50 = ₹ 0.50
Gain percent = (gain × 100)/ C.P
Substituting the values
= 0.50/3.50 × 100%
= 14 2/7 %
Exercise 9C page: 109
1. A machine is marked at ₹ 5,000 and is sold at a discount of 10%. Find the selling price of the machine.
Solution:
It is given that
M.P of the machine = ₹ 5, 000
Rate of discount = 10%
So the amount of discount = 5000 × 10/100 = ₹ 500
S.P = M.P – discount
Substituting the values
= 5000 – 500
= ₹ 4500
2. A shopkeeper marked a dinner set for ₹ 1,000. He sold it at ₹ 900. What percent discount did he give?
Solution:
It is given that
M.P of a dinner set = ₹ 1000
S.P of a dinner set = ₹ 900
So the amount of discount = 1000 – 900 = ₹ 100
Discount percent = (Discount × 100)/ M.P
Substituting the values
= (100 × 100)/ 1000
= 10%
3. A pair of shoes, marked at ₹ 320, are sold at a discount of 15 percent.
Find:
(i) the discount,
(ii) the selling price of the shoes.
Solution:
It is given that
M.P of shoes = ₹ 320
Rate of discount = 15%
(i) Amount of discount = (320 × 15)/ 100 = ₹ 48
(ii) S.P = M.P – Discount
Substituting the values
= 320 – 48
= ₹ 272
4. The list price of an article is ₹ 450 and it is sold for ₹ 360.
Find:
(i) the discount,
(ii) the discount percent.
Solution:
It is given that
M.P of an article = ₹ 450
S.P of an article = ₹ 360
(i) Amount of discount = M.P – S.P
Substituting the values
= 450 – 360
= ₹ 90
(ii) Discount percent = (discount × 100)/ M.P
Substituting the values
= (90 × 100)/ 450
= 20%
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) the profit percent made by the shopkeeper.
Solution:
It is given that
C.P of an article = ₹ 300
Increase in price = 20%
(i) M.P = [C.P (100 + increase percent)]/ 100
Substituting the values
= [300 (100 + 20)]/ 100
So we get
= (300 × 120)/ 100
= ₹ 360
(ii) Rate of discount = 10%
Amount of discount = (360 × 10)/ 100 = ₹ 36
(iii) S.P = M.P – discount
Substituting the values
= 360 – 36
= ₹ 324
(iv) Net profit made by the shopkeeper = S.P – C.P
Substituting the values
= 324 – 300
= ₹ 24
We know that
Gain percent = (gain × 100)/ C.P
Substituting the values
= (24 × 100)/ 300
= 8%
6. A car is marked at ₹ 50,000. The dealer gives 5% discount on first ₹ 20,000 and 2% discount on the remaining ₹ 30,000. Find:
(i) the total discount.
(ii) the price charged by the dealer.
Solution:
It is given that
M.P of a car = ₹ 50,000
Discount at the rate of 5% on first ₹ 20,000 = (20,000 × 5)/ 100 = ₹ 1000
Discount at the rate of 2% on remaining ₹ 30,000 = (30,000 × 2)/ 100 = ₹ 600
(i) Total discount = 1000 + 600 = ₹ 1600
(ii) Price charged by the dealer = 50000 – 1600 = ₹ 48400
7. A dealer buys a T.V. set for ₹ 2,500. He marks it at ₹ 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.
Solution:
It is given that
C.P of a T.V. set = ₹ 2,500
M.P of a T.V. set = ₹ 3,200
Rate of discount = 10%
So the total discount = 3200 × 10/100 = ₹ 320
(i) S.P of the TV set = 3200 – 320 = ₹ 2880
(ii) Gain = S.P – C.P
Substituting the values
= 2880 – 2500
= ₹ 380
Gain percent = (gain × 100)/ C.P
Substituting the values
= (380 × 100)/ 2500
= 76/5
= 15 1/5 % or 15.2%
8. A sells his goods at 15% discount. Find the price of an article which is sold for ₹ 680.
Solution:
It is given that
S.P of an article = ₹ 680
Rate of discount = 15%
Consider M.P of the article = ₹ 100
S.P = 100 – 15 = ₹ 85
If S.P of the article is ₹ 85 then M.P = ₹ 100
If S.P of the article is ₹ 680 then M.P = (100 × 680)/ 85 = ₹ 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 ₹ 560.
Solution:
Consider M.P of articles = ₹ 100
Discount on the M.P = 20%
S.P of articles = 100 – 20 = ₹ 80
If S.P of articles is ₹ 80 then M.P = ₹ 100
If S.P of articles is ₹ 560 then M.P = (100 × 560)/ 80 = ₹ 700
10. An article is bought for ₹ 1,200 and ₹ 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.
Solution:
It is given that
C.P of an article = ₹ 1200
Amount spent on transportation = ₹ 100
(i) Total C.P of the article = 1200 + 100 = ₹ 1300
(ii) Gain = 20%
S.P = [C.P (100 + gain percent)]/ 100
Substituting the values
= [1300 (100 + 20)]/ 100
So we get
= (1300 × 120)/ 100
= ₹ 1560
11. 40 pens are bought at 4 for ₹ 50 and all of them are sold at 5 for ₹ 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?
Solution:
(i) C.P of 4 pens = ₹ 50
C.P of 40 pens = (50 × 40)/ 4 = ₹ 500
So the C.P of 1 pen = 500/40 = 25/2 = ₹ 12.50
(ii) S.P of pens = ₹ 80
So the S.P of one pen = 80/5 = ₹ 16
(iii) Profit made by selling one pen = S.P – C.P
Substituting the values
= 16 – 12.50
= ₹ 3.50
(iv) Profit percent made by selling one pen = (profit × 100)/ C.P
Substituting the values
= (3.50 × 100)/ 12.50
Multiplying both numerator and denominator by 100
= (350 × 100)/ 1250
= 28%
(v) C.P of 40 pens = 40 × 12.50 = ₹ 500
(vi) S.P of 40 pens = 40 × 16 = ₹ 640
(vii) Profit made by selling 40 pens = S.P – C.P
Substituting the values
= 640 – 500
= ₹ 140
(viii) Profit percent made by selling 40 pens = (profit × 100)/ C.P
Substituting the values
= (140 × 100)/ 500
= 28%
Yes, the results of (iv) and (viii) are same.
Here we get to know that the profit of 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 have been sold.
Solution:
It is given that
C.P of 5 articles = S.P of 4 articles
Consider the C.P of 5 articles = S.P of 4 articles = ₹ 100
C.P of 1 article = 100/5 = ₹ 20
S.P of 1 article = 100/4 = ₹ 25
Profit = S.P – C.P
Substituting the values
= 25 – 20
= ₹ 5
Profit percent = (profit × 100)/ C.P
Substituting the values
= (5 × 100)/ 20
= 25%
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.
Solution:
Consider C.P of 8 pens = S.P of 10 pens = ₹ 100
C.P of 1 pen = 100.8 = ₹ 12.50
S.P of 1 pen = 100/10 = ₹ 10
Loss = C.P – S.P
Substituting the values
= 12.50 – 10
= ₹ 2.50
Loss percent = (loss × 100)/ C.P
Substituting the values
= (2.50 × 100)/ 12.50
Multiplying both numerator and denominator by 100 × 100
= (250 × 100 × 100)/ (1250 × 100)
= 20%
14. A certain number of articles are bought at ₹ 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.
Solution:
It is given that
C.P of 1 dozen articles = ₹ 450
Profit = 20%
S.P = [C.P (100 + profit)]/ 100
Substituting the values
= [450 (100 + 20)]/ 100
So we get
= (450 × 120)/ 100
= ₹ 540
(i) S.P of one article = 540/12 = ₹ 45
(ii) S.P of seven articles = 45 × 7 = ₹ 315
15. An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Solution:
Consider the C.P of an article = ₹ 100
M.P of an article = 100 + 60 = ₹ 160
Rate of discount = 20%
S.P = [M.P (100 – Discount percent)]/ 100
Substituting the values
= [160 (100 – 20)]/ 100
So we get
= (160 × 80)/ 100
= ₹ 128
Profit = S.P – C.P
Substituting the values
= 128 – 100
= ₹ 28
Profit percent = (profit × 100)/ C.P
Substituting the values
= (28 × 100)/ 100
= 28%
Exercise 9B
Exercise 9B page: 107
1. Find the cost price, if:
(i) S.P. = ₹ 21 and gain = 5%
(ii) S.P. = ₹ 22 and loss = 12%
(iii) S.P. = ₹ 340 and gain = ₹ 20
(iv) S.P. = ₹ 200 and loss = ₹ 50
(v) S.P. = ₹ 1 and loss = 5 p
Solution:
(i) S.P. = ₹ 21 and gain = 5%
We know that
C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (21 × 100)/ (100 + 5)
= (21 × 100)/ 105
So we get
= ₹ 20
(ii) S.P. = ₹ 22 and loss = 12%
We know that
C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (22 × 100)/ (100 – 12)
= (22 × 100)/ 88
So we get
= ₹ 25
(iii) S.P. = ₹ 340 and gain = ₹ 20
We know that
C.P. = S.P. – Gain
Substituting the values
= 340 – 20
= ₹ 320
(iv) S.P. = ₹ 200 and loss = ₹ 50
We know that
C.P. = S.P. + loss
Substituting the values
= 200 + 50
= ₹ 250
(v) S.P. = ₹ 1 and loss = 5 p
We know that
C.P. = S.P. + Loss
Substituting the values
= ₹ 1 + 5 p
= ₹ 1.05
2. By selling an article for ₹ 810, a loss of percent is suffered. Find its cost price.
Solution:
It is given that
S.P of an article = ₹ 810
Loss percent = 10 %
We know that
C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (810 × 100)/ (100 – 10)
So we get
= (810 × 100)/ 90
= ₹ 900
3. By selling a scooter for ₹ 9,200, a main gains 15%. Find the cost price of the scooter.
Solution:
It is given that
S.P. of the scooter = ₹ 9,200
Gain percent = 15%
We know that
C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (9200 × 100)/ (100 + 15)
= (9200 × 100)/ 115
So we get
= ₹ 8000
4. On selling an article for ₹ 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%.
Solution:
It is given that
S.P. of an article = ₹ 2,640
Gain percent = 10%
(i) C.P. = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (2640 × 100)/ (100 + 10)
= (2640 × 100)/ 110
So we get
= ₹ 2400
(ii) Gain percent = 15%
S.P. = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [2400 (100 + 15)]/ 100
So we get
= (2400 × 115)/ 100
= ₹ 2760
5. A T.V. set is sold for ₹ 6,800 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%.
Solution:
It is given that
S.P. of the T.V. set = ₹ 6,800
Loss percent = 15%
(i) C.P. = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (6800 × 100)/ (100 – 15)
So we get
= (6800 × 100)/ 85
= ₹ 8000
(ii) Gain percent = 12%
We know that
S.P. = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [8000 (100 + 12)]/ 100
So we get
= (8000 × 112)/ 100
= ₹ 8960
6. A fruit seller bought mangoes at ₹ 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
Solution:
It is given that
C.P. of 1 dozen mangoes = ₹ 90
Loss percent = 8%
Here the S.P of 1 dozen mangoes = [C.P. (100 – loss percent)]/ 100
Substituting the values
= [900 (100 – 8)]/ 100
So we get
= (90 × 92)/ 100
= ₹ 82.80
(i) S.P. of one mango = 82.80/12 = ₹ 6.90
(ii) S.P. of 40 mangoes = 6.90 × 40 = ₹ 276
7. By selling two transistors for ₹ 600 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.
Solution:
It is given that
S.P of first transistor = ₹ 600
Gain percent = 20%
(i) C.P = (S.P. × 100)/ (100 + gain percent)
Substituting the values
= (600 × 100)/ (100 + 20)
= (600 × 100)/ 120
So we get
= ₹ 500
S.P of the second transistor = ₹ 600
Loss percent = 20%
So the C.P of the other transistor = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (600 × 100)/ (100 – 20)
So we get
= (600 × 100)/ 80
= ₹ 750
Hence, C.P of the two transistors are ₹ 500 and ₹ 750.
(ii) Total C.P of both the transistors = 500 + 750 = ₹ 1250
Total S.P of both the transistors = 600 + 600 = ₹ 1200
(iii) We know that
Total loss = C.P – S.P
Substituting the values
= 1250 – 1200
= ₹ 50
So the loss percent = (loss × 100)/ C.P
Substituting the values
= (50 × 100)/ 1250
= 4%
8. Mangoes are bought at 20 for ₹ 60. If they are sold at a profit of 33 1/3 percent, find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Solution:
It is given that
C.P of 20 mangoes = ₹ 60
Gain percent = 33 1/3 % = 100/3 %
S.P of 20 mangoes = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [60 (100 + 100/3)]/ 100
So we get
= (60 × 400)/ (100 × 3)
= ₹ 80
(i) S.P of one mango = 80/20 = ₹ 4
(ii) S.P of 8 mangoes = 4 × 8 = ₹ 32
9. Find the cost price of an article, which is sold for ₹ 4,050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Solution:
It is given that
S.P of an article = ₹ 4,050
Loss percent = 10%
(i) C.P of the article = (S.P. × 100)/ (100 – loss percent)
Substituting the values
= (4050 × 100)/ (100 – 10)
So we get
= (4050 × 100)/ 90
= ₹ 4500
(ii) Gain percent = 8%
S.P of the article = [C.P. (100 + gain percent)]/ 100
Substituting the values
= [4500 (100 + 8)]/ 100
So we get
= (4500 × 108)/ 100
= ₹ 4860
10. By selling an article for ₹ 825, a man losses an amount equal to 1/3 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 ₹ 1,265.
Solution:
It is given that
S.P of an article = ₹ 825
Loss = 1/3 of S.P = 1/3 × 825 = ₹ 275
(i) C.P = S.P + Loss
Substituting the values
= 825 + 275
= ₹ 1100
(ii) S.P = ₹ 1265
We know that
Gain = S.P – C.P
Substituting the values
= 1265 – 1100
= ₹ 165
Gain percent = (gain × 100)/ C.P
Substituting the values
= (165 × 100)/ 1100
= 15%
11. Find the loss or gain as percent, if the C.P. of articles, all of the same kind, is equal to S.P. of 8 articles.
Solution:
Consider C.P of 10 articles = S.P of 8 articles = ₹ 80
So the C.P of 1 article = 80/10 = ₹ 8
S.P of 1 article = 80/8 = ₹ 10
We know that
Gain = S.P – C.P
Substituting the values
= 10 – 8
= ₹ 2
Gain percent = (gain × 100)/ C.P
Substituting the values
= (2 × 100)/ 8
= 25%
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.
Solution:
Consider C.P of 8 articles = S.P of 10 articles = ₹ 80
So the C.P of 1 article = 80/8 = ₹ 10
S.P of 1 article = 80/10 = ₹ 8
We know that
Loss = C.P – S.P
Substituting the values
= 10 – 8
= ₹ 2
Loss percent = (loss × 100)/ C.P
Substituting the values
= (2 × 100)/ 10
= 20%
13. The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Solution:
Consider S.P = ₹ 100
We know that
C.P = 96% of S.P
So we get
= 96/100 × 100
= ₹ 96
Gain = 100 – 96 = ₹ 4
Gain percent = (gain × 100)/ C.P
Substituting the values
= 4/96 × 100%
= 25/6 or 4 1/6%
14. The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Solution:
Consider C.P = ₹ 100
S.P = 96% of C.P
So we get
= 96/100 × 100
= ₹ 96
Loss = 100 – 96 = ₹ 4
Loss percent = (loss × 100)/ C.P
Substituting the values
= 4/100 × 100%
= 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.
Solution:
It is given that
C.P of one orange = 350/100 = ₹ 3.50
S.P of one orange = 48/12 = ₹ 4
Gain = 4 – 3.50 = ₹ 0.50
Gain percent = (gain × 100)/ C.P
Substituting the values
= 0.50/3.50 × 100%
= 14 2/7 %
Exercise 9C
Exercise 9C page: 109
1. A machine is marked at ₹ 5,000 and is sold at a discount of 10%. Find the selling price of the machine.
Solution:
It is given that
M.P of the machine = ₹ 5, 000
Rate of discount = 10%
So the amount of discount = 5000 × 10/100 = ₹ 500
S.P = M.P – discount
Substituting the values
= 5000 – 500
= ₹ 4500
2. A shopkeeper marked a dinner set for ₹ 1,000. He sold it at ₹ 900. What percent discount did he give?
Solution:
It is given that
M.P of a dinner set = ₹ 1000
S.P of a dinner set = ₹ 900
So the amount of discount = 1000 – 900 = ₹ 100
Discount percent = (Discount × 100)/ M.P
Substituting the values
= (100 × 100)/ 1000
= 10%
3. A pair of shoes, marked at ₹ 320, are sold at a discount of 15 percent.
Find:
(i) the discount,
(ii) the selling price of the shoes.
Solution:
It is given that
M.P of shoes = ₹ 320
Rate of discount = 15%
(i) Amount of discount = (320 × 15)/ 100 = ₹ 48
(ii) S.P = M.P – Discount
Substituting the values
= 320 – 48
= ₹ 272
4. The list price of an article is ₹ 450 and it is sold for ₹ 360.
Find:
(i) the discount,
(ii) the discount percent.
Solution:
It is given that
M.P of an article = ₹ 450
S.P of an article = ₹ 360
(i) Amount of discount = M.P – S.P
Substituting the values
= 450 – 360
= ₹ 90
(ii) Discount percent = (discount × 100)/ M.P
Substituting the values
= (90 × 100)/ 450
= 20%
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) the profit percent made by the shopkeeper.
Solution:
It is given that
C.P of an article = ₹ 300
Increase in price = 20%
(i) M.P = [C.P (100 + increase percent)]/ 100
Substituting the values
= [300 (100 + 20)]/ 100
So we get
= (300 × 120)/ 100
= ₹ 360
(ii) Rate of discount = 10%
Amount of discount = (360 × 10)/ 100 = ₹ 36
(iii) S.P = M.P – discount
Substituting the values
= 360 – 36
= ₹ 324
(iv) Net profit made by the shopkeeper = S.P – C.P
Substituting the values
= 324 – 300
= ₹ 24
We know that
Gain percent = (gain × 100)/ C.P
Substituting the values
= (24 × 100)/ 300
= 8%
6. A car is marked at ₹ 50,000. The dealer gives 5% discount on first ₹ 20,000 and 2% discount on the remaining ₹ 30,000. Find:
(i) the total discount.
(ii) the price charged by the dealer.
Solution:
It is given that
M.P of a car = ₹ 50,000
Discount at the rate of 5% on first ₹ 20,000 = (20,000 × 5)/ 100 = ₹ 1000
Discount at the rate of 2% on remaining ₹ 30,000 = (30,000 × 2)/ 100 = ₹ 600
(i) Total discount = 1000 + 600 = ₹ 1600
(ii) Price charged by the dealer = 50000 – 1600 = ₹ 48400
7. A dealer buys a T.V. set for ₹ 2,500. He marks it at ₹ 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.
Solution:
It is given that
C.P of a T.V. set = ₹ 2,500
M.P of a T.V. set = ₹ 3,200
Rate of discount = 10%
So the total discount = 3200 × 10/100 = ₹ 320
(i) S.P of the TV set = 3200 – 320 = ₹ 2880
(ii) Gain = S.P – C.P
Substituting the values
= 2880 – 2500
= ₹ 380
Gain percent = (gain × 100)/ C.P
Substituting the values
= (380 × 100)/ 2500
= 76/5
= 15 1/5 % or 15.2%
8. A sells his goods at 15% discount. Find the price of an article which is sold for ₹ 680.
Solution:
It is given that
S.P of an article = ₹ 680
Rate of discount = 15%
Consider M.P of the article = ₹ 100
S.P = 100 – 15 = ₹ 85
If S.P of the article is ₹ 85 then M.P = ₹ 100
If S.P of the article is ₹ 680 then M.P = (100 × 680)/ 85 = ₹ 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 ₹ 560.
Solution:
Consider M.P of articles = ₹ 100
Discount on the M.P = 20%
S.P of articles = 100 – 20 = ₹ 80
If S.P of articles is ₹ 80 then M.P = ₹ 100
If S.P of articles is ₹ 560 then M.P = (100 × 560)/ 80 = ₹ 700
10. An article is bought for ₹ 1,200 and ₹ 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.
Solution:
It is given that
C.P of an article = ₹ 1200
Amount spent on transportation = ₹ 100
(i) Total C.P of the article = 1200 + 100 = ₹ 1300
(ii) Gain = 20%
S.P = [C.P (100 + gain percent)]/ 100
Substituting the values
= [1300 (100 + 20)]/ 100
So we get
= (1300 × 120)/ 100
= ₹ 1560
11. 40 pens are bought at 4 for ₹ 50 and all of them are sold at 5 for ₹ 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?
Solution:
(i) C.P of 4 pens = ₹ 50
C.P of 40 pens = (50 × 40)/ 4 = ₹ 500
So the C.P of 1 pen = 500/40 = 25/2 = ₹ 12.50
(ii) S.P of pens = ₹ 80
So the S.P of one pen = 80/5 = ₹ 16
(iii) Profit made by selling one pen = S.P – C.P
Substituting the values
= 16 – 12.50
= ₹ 3.50
(iv) Profit percent made by selling one pen = (profit × 100)/ C.P
Substituting the values
= (3.50 × 100)/ 12.50
Multiplying both numerator and denominator by 100
= (350 × 100)/ 1250
= 28%
(v) C.P of 40 pens = 40 × 12.50 = ₹ 500
(vi) S.P of 40 pens = 40 × 16 = ₹ 640
(vii) Profit made by selling 40 pens = S.P – C.P
Substituting the values
= 640 – 500
= ₹ 140
(viii) Profit percent made by selling 40 pens = (profit × 100)/ C.P
Substituting the values
= (140 × 100)/ 500
= 28%
Yes, the results of (iv) and (viii) are same.
Here we get to know that the profit of 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 have been sold.
Solution:
It is given that
C.P of 5 articles = S.P of 4 articles
Consider the C.P of 5 articles = S.P of 4 articles = ₹ 100
C.P of 1 article = 100/5 = ₹ 20
S.P of 1 article = 100/4 = ₹ 25
Profit = S.P – C.P
Substituting the values
= 25 – 20
= ₹ 5
Profit percent = (profit × 100)/ C.P
Substituting the values
= (5 × 100)/ 20
= 25%
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.
Solution:
Consider C.P of 8 pens = S.P of 10 pens = ₹ 100
C.P of 1 pen = 100.8 = ₹ 12.50
S.P of 1 pen = 100/10 = ₹ 10
Loss = C.P – S.P
Substituting the values
= 12.50 – 10
= ₹ 2.50
Loss percent = (loss × 100)/ C.P
Substituting the values
= (2.50 × 100)/ 12.50
Multiplying both numerator and denominator by 100 × 100
= (250 × 100 × 100)/ (1250 × 100)
= 20%
14. A certain number of articles are bought at ₹ 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.
Solution:
It is given that
C.P of 1 dozen articles = ₹ 450
Profit = 20%
S.P = [C.P (100 + profit)]/ 100
Substituting the values
= [450 (100 + 20)]/ 100
So we get
= (450 × 120)/ 100
= ₹ 540
(i) S.P of one article = 540/12 = ₹ 45
(ii) S.P of seven articles = 45 × 7 = ₹ 315
15. An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Solution:
Consider the C.P of an article = ₹ 100
M.P of an article = 100 + 60 = ₹ 160
Rate of discount = 20%
S.P = [M.P (100 – Discount percent)]/ 100
Substituting the values
= [160 (100 – 20)]/ 100
So we get
= (160 × 80)/ 100
= ₹ 128
Profit = S.P – C.P
Substituting the values
= 128 – 100
= ₹ 28
Profit percent = (profit × 100)/ C.P
Substituting the values
= (28 × 100)/ 100
= 28%
Download PDF
Selina Class 7 ICSE Solutions Mathematics : Chapter 9- Profit, Loss and Discount
Download PDF: Selina Class 7 ICSE Solutions Mathematics : Chapter 9- Profit, Loss and Discount PDF
Chapterwise Selina Publishers ICSE Solutions for Class 7 Mathematics :
- Chapter 1- Integers
- Chapter 2- Rational Numbers
- Chapter 3- Fraction (Including Problems)
- Chapter 4- Decimal Fractions (Decimals)
- Chapter 5- Exponents (Including Laws of Exponents)
- Chapter 6- Ratio and Proportion (Including Sharing in a Ratio)
- Chapter 7- Unitary Method (Including Time and Work)
- Chapter 8- Percent and Percentage
- Chapter 9- Profit, Loss and Discount
- Chapter 10- Simple Interest
- Chapter 11- Fundamental Concepts (Including Fundamental Operations)
- Chapter 12- Simple Linear Equations (Including Word Problems)
- Chapter 13- Set Concepts
- Chapter 14- Lines and Angles (Including Construction of Angles)
- Chapter 15- Triangles
- Chapter 16- Pythagoras Theorem
- Chapter 17- Symmetry (Including Reflection and Rotation)
- Chapter 18- Recognition of Solids (Representing 3-D in 2-D)
- Chapter 19- Congruency: Congruent Triangles
- Chapter 20- Mensuration (Perimeter and Area of Plane Figures)
- Chapter 21- Data Handling
- Chapter 22- Probability
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