Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Profit, Loss, Discount and Value Added Tax (VAT) - Exercise 13.1
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Page 1
EXERCISE 13.1 PAGE NO: 13.11
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain
percent.
Solution:
We know that the cost price of pen = Rs 90
Selling price of pen = Rs 100
By using the formula,
Gain = selling price – cost price
= 100 – 90
= Rs 10
By using the formula,
Gain % = (gain/cost price) × 100
= (10/90) × 100
= 100/9
= 11 1/9 %
2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss
percent.
Solution:
We know that the cost price of saree = Rs 1240
Selling price of saree = Rs 1147
By using the formula,
Loss = cost price – selling price
= 1240 – 1147
= Rs 93
By using the formula,
Loss % = (loss/cost price) × 100
= (93/1240) × 100
= 7.5 %
3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or
loss percent.
Solution:
We know that the cost price of 9 apples = Rs 9.60
Cost price of 1 apple = Rs 9.60/9
Selling price of 11 apple = Rs 12
Selling price of 1 apple = Rs 12/11
By using the formula,
Page 2
EXERCISE 13.1 PAGE NO: 13.11
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain
percent.
Solution:
We know that the cost price of pen = Rs 90
Selling price of pen = Rs 100
By using the formula,
Gain = selling price – cost price
= 100 – 90
= Rs 10
By using the formula,
Gain % = (gain/cost price) × 100
= (10/90) × 100
= 100/9
= 11 1/9 %
2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss
percent.
Solution:
We know that the cost price of saree = Rs 1240
Selling price of saree = Rs 1147
By using the formula,
Loss = cost price – selling price
= 1240 – 1147
= Rs 93
By using the formula,
Loss % = (loss/cost price) × 100
= (93/1240) × 100
= 7.5 %
3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or
loss percent.
Solution:
We know that the cost price of 9 apples = Rs 9.60
Cost price of 1 apple = Rs 9.60/9
Selling price of 11 apple = Rs 12
Selling price of 1 apple = Rs 12/11
By using the formula,
Gain = selling price – cost price
= 12/11 – 9.60/9
= (108-105.60)/99
= Rs 2.40/99
By using the formula,
Gain % = (gain/cost price) × 100
= ((2.40/99)/(9.60/9)) × 100
= 25/11
= 2 3/11%
4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the
profit percent.
Solution:
We know that the cost price of 10 article = selling price of 9 article
Let us consider CP of 1 article as Rs X
Selling price of 9 article = 10X
Selling price of 1 article = 10x/9
Profit = 10x/9 – x
= x/9
Profit % = Gain % = (gain/cost price) × 100
= (x/9)/x × 100
= 100/9
= 11 1/9%
5. A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the
radio for Rs 300, determine his profit percent.
Solution:
The cost price of a radio = Rs 225
Overhead expenses = Rs 15
Total cost = cost price + overhead expenses = 225+15 = Rs 240
Selling price of radio = Rs.300
By using the formula,
Gain = selling price – cost price
= 300 – 240 = Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
Page 3
EXERCISE 13.1 PAGE NO: 13.11
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain
percent.
Solution:
We know that the cost price of pen = Rs 90
Selling price of pen = Rs 100
By using the formula,
Gain = selling price – cost price
= 100 – 90
= Rs 10
By using the formula,
Gain % = (gain/cost price) × 100
= (10/90) × 100
= 100/9
= 11 1/9 %
2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss
percent.
Solution:
We know that the cost price of saree = Rs 1240
Selling price of saree = Rs 1147
By using the formula,
Loss = cost price – selling price
= 1240 – 1147
= Rs 93
By using the formula,
Loss % = (loss/cost price) × 100
= (93/1240) × 100
= 7.5 %
3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or
loss percent.
Solution:
We know that the cost price of 9 apples = Rs 9.60
Cost price of 1 apple = Rs 9.60/9
Selling price of 11 apple = Rs 12
Selling price of 1 apple = Rs 12/11
By using the formula,
Gain = selling price – cost price
= 12/11 – 9.60/9
= (108-105.60)/99
= Rs 2.40/99
By using the formula,
Gain % = (gain/cost price) × 100
= ((2.40/99)/(9.60/9)) × 100
= 25/11
= 2 3/11%
4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the
profit percent.
Solution:
We know that the cost price of 10 article = selling price of 9 article
Let us consider CP of 1 article as Rs X
Selling price of 9 article = 10X
Selling price of 1 article = 10x/9
Profit = 10x/9 – x
= x/9
Profit % = Gain % = (gain/cost price) × 100
= (x/9)/x × 100
= 100/9
= 11 1/9%
5. A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the
radio for Rs 300, determine his profit percent.
Solution:
The cost price of a radio = Rs 225
Overhead expenses = Rs 15
Total cost = cost price + overhead expenses = 225+15 = Rs 240
Selling price of radio = Rs.300
By using the formula,
Gain = selling price – cost price
= 300 – 240 = Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25 %
6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he
sells the cooler for Rs 1550, determine his profit percent.
Solution:
We know the cost price of cooler = Rs 1200
Overhead expenses = Rs 40
Total cost = Rs 1200 + Rs 40 = Rs 1240
Selling price of cooler = Rs 1550
By using the formula,
Gain = selling price – cost price
= Rs 1550 - Rs1240
= Rs 310
By using the formula,
Gain % = (gain/cost price) × 100
= 310/1240 × 100
= 25%
7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells
the same for Rs 300, find his profit percent.
Solution:
We know the cost price of wrist watch = Rs 225
Cost of repairing = Rs 15
Total cost = Rs 225 + Rs 15 = Rs 240
Selling price of watch = Rs 300
By using the formula,
Gain = selling price – cost price
= Rs 300 – Rs 240
= Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25%
8. Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the
other box at a loss of 12%. If the selling price of both boxes is the same, find the cost
price of each box.
Solution:
Page 4
EXERCISE 13.1 PAGE NO: 13.11
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain
percent.
Solution:
We know that the cost price of pen = Rs 90
Selling price of pen = Rs 100
By using the formula,
Gain = selling price – cost price
= 100 – 90
= Rs 10
By using the formula,
Gain % = (gain/cost price) × 100
= (10/90) × 100
= 100/9
= 11 1/9 %
2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss
percent.
Solution:
We know that the cost price of saree = Rs 1240
Selling price of saree = Rs 1147
By using the formula,
Loss = cost price – selling price
= 1240 – 1147
= Rs 93
By using the formula,
Loss % = (loss/cost price) × 100
= (93/1240) × 100
= 7.5 %
3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or
loss percent.
Solution:
We know that the cost price of 9 apples = Rs 9.60
Cost price of 1 apple = Rs 9.60/9
Selling price of 11 apple = Rs 12
Selling price of 1 apple = Rs 12/11
By using the formula,
Gain = selling price – cost price
= 12/11 – 9.60/9
= (108-105.60)/99
= Rs 2.40/99
By using the formula,
Gain % = (gain/cost price) × 100
= ((2.40/99)/(9.60/9)) × 100
= 25/11
= 2 3/11%
4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the
profit percent.
Solution:
We know that the cost price of 10 article = selling price of 9 article
Let us consider CP of 1 article as Rs X
Selling price of 9 article = 10X
Selling price of 1 article = 10x/9
Profit = 10x/9 – x
= x/9
Profit % = Gain % = (gain/cost price) × 100
= (x/9)/x × 100
= 100/9
= 11 1/9%
5. A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the
radio for Rs 300, determine his profit percent.
Solution:
The cost price of a radio = Rs 225
Overhead expenses = Rs 15
Total cost = cost price + overhead expenses = 225+15 = Rs 240
Selling price of radio = Rs.300
By using the formula,
Gain = selling price – cost price
= 300 – 240 = Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25 %
6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he
sells the cooler for Rs 1550, determine his profit percent.
Solution:
We know the cost price of cooler = Rs 1200
Overhead expenses = Rs 40
Total cost = Rs 1200 + Rs 40 = Rs 1240
Selling price of cooler = Rs 1550
By using the formula,
Gain = selling price – cost price
= Rs 1550 - Rs1240
= Rs 310
By using the formula,
Gain % = (gain/cost price) × 100
= 310/1240 × 100
= 25%
7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells
the same for Rs 300, find his profit percent.
Solution:
We know the cost price of wrist watch = Rs 225
Cost of repairing = Rs 15
Total cost = Rs 225 + Rs 15 = Rs 240
Selling price of watch = Rs 300
By using the formula,
Gain = selling price – cost price
= Rs 300 – Rs 240
= Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25%
8. Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the
other box at a loss of 12%. If the selling price of both boxes is the same, find the cost
price of each box.
Solution:
We know the cost price of two boxes = Rs 1300
So let us consider cost price of one box be Rs x
Cost price of other box = Rs 1300 – x
Selling price of first box = x + x × 20/100
= x + x/5
= Rs 6x/5
Selling price of second box = (1300 - x) – (1300 - x) × 12/100
= Rs (28600 – 22x)/25
By equating SP of first and second box we get,
6x/5 = (28600 – 22x)/25
150x = 28600 × 5 – 110x
150x + 110x = 28600 × 5
260x = 28600 × 5
x = (28600 × 5)/260
= 550
? Cost price of first box = Rs. 550
Cost price of second box = Rs1300 – Rs550 = Rs 750
9. If the selling price of 10 pens is equal to cost price of 14 pens, find the gain
percent.
Solution:
Given that, Selling price of 10 pens = cost price of 14 pens
So, let the cost price of 1 pen be Rs x
Selling price of 10 pens = Rs 14x
Selling price of 1 pen =Rs 14x/10
By using the formula,
Gain = selling price – cost price
= 14x/10 – x
= 4x/10
By using the formula,
Gain % = (gain/cost price) × 100
= (4x/10)/x × 100
= 2/5 × 100
= 40%
10. If the selling price of 18 chairs be equal to selling price of 16 chairs, find the gain
or loss percent.
Page 5
EXERCISE 13.1 PAGE NO: 13.11
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain
percent.
Solution:
We know that the cost price of pen = Rs 90
Selling price of pen = Rs 100
By using the formula,
Gain = selling price – cost price
= 100 – 90
= Rs 10
By using the formula,
Gain % = (gain/cost price) × 100
= (10/90) × 100
= 100/9
= 11 1/9 %
2. Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss
percent.
Solution:
We know that the cost price of saree = Rs 1240
Selling price of saree = Rs 1147
By using the formula,
Loss = cost price – selling price
= 1240 – 1147
= Rs 93
By using the formula,
Loss % = (loss/cost price) × 100
= (93/1240) × 100
= 7.5 %
3. A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or
loss percent.
Solution:
We know that the cost price of 9 apples = Rs 9.60
Cost price of 1 apple = Rs 9.60/9
Selling price of 11 apple = Rs 12
Selling price of 1 apple = Rs 12/11
By using the formula,
Gain = selling price – cost price
= 12/11 – 9.60/9
= (108-105.60)/99
= Rs 2.40/99
By using the formula,
Gain % = (gain/cost price) × 100
= ((2.40/99)/(9.60/9)) × 100
= 25/11
= 2 3/11%
4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the
profit percent.
Solution:
We know that the cost price of 10 article = selling price of 9 article
Let us consider CP of 1 article as Rs X
Selling price of 9 article = 10X
Selling price of 1 article = 10x/9
Profit = 10x/9 – x
= x/9
Profit % = Gain % = (gain/cost price) × 100
= (x/9)/x × 100
= 100/9
= 11 1/9%
5. A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the
radio for Rs 300, determine his profit percent.
Solution:
The cost price of a radio = Rs 225
Overhead expenses = Rs 15
Total cost = cost price + overhead expenses = 225+15 = Rs 240
Selling price of radio = Rs.300
By using the formula,
Gain = selling price – cost price
= 300 – 240 = Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25 %
6. A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he
sells the cooler for Rs 1550, determine his profit percent.
Solution:
We know the cost price of cooler = Rs 1200
Overhead expenses = Rs 40
Total cost = Rs 1200 + Rs 40 = Rs 1240
Selling price of cooler = Rs 1550
By using the formula,
Gain = selling price – cost price
= Rs 1550 - Rs1240
= Rs 310
By using the formula,
Gain % = (gain/cost price) × 100
= 310/1240 × 100
= 25%
7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells
the same for Rs 300, find his profit percent.
Solution:
We know the cost price of wrist watch = Rs 225
Cost of repairing = Rs 15
Total cost = Rs 225 + Rs 15 = Rs 240
Selling price of watch = Rs 300
By using the formula,
Gain = selling price – cost price
= Rs 300 – Rs 240
= Rs 60
By using the formula,
Gain % = (gain/cost price) × 100
= 60/240 × 100
= 25%
8. Ramesh bought two boxes for Rs 1300. He sold one box at a profit of 20% and the
other box at a loss of 12%. If the selling price of both boxes is the same, find the cost
price of each box.
Solution:
We know the cost price of two boxes = Rs 1300
So let us consider cost price of one box be Rs x
Cost price of other box = Rs 1300 – x
Selling price of first box = x + x × 20/100
= x + x/5
= Rs 6x/5
Selling price of second box = (1300 - x) – (1300 - x) × 12/100
= Rs (28600 – 22x)/25
By equating SP of first and second box we get,
6x/5 = (28600 – 22x)/25
150x = 28600 × 5 – 110x
150x + 110x = 28600 × 5
260x = 28600 × 5
x = (28600 × 5)/260
= 550
? Cost price of first box = Rs. 550
Cost price of second box = Rs1300 – Rs550 = Rs 750
9. If the selling price of 10 pens is equal to cost price of 14 pens, find the gain
percent.
Solution:
Given that, Selling price of 10 pens = cost price of 14 pens
So, let the cost price of 1 pen be Rs x
Selling price of 10 pens = Rs 14x
Selling price of 1 pen =Rs 14x/10
By using the formula,
Gain = selling price – cost price
= 14x/10 – x
= 4x/10
By using the formula,
Gain % = (gain/cost price) × 100
= (4x/10)/x × 100
= 2/5 × 100
= 40%
10. If the selling price of 18 chairs be equal to selling price of 16 chairs, find the gain
or loss percent.
Solution:
Given that, Cost price of 18 chairs = selling price of 16 chairs
So, let the cost price of 1 chair be Rs x
Selling price of 16 chairs =Rs 18x
Selling price of 1 chair = Rs 18x/16
By using the formula,
Gain = selling price – cost price
= 18x/16 – x
= 2x/16
= Rs x/8
By using the formula,
Gain % = (gain/cost price) × 100
= (x/8)/x × 100
= 25/2
= 12 ½ %
11. If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the
loss percent.
Solution:
Given that, Selling price of 18 oranges = cost price of 16 oranges
So, let the cost price of 1 orange be Rs x
Selling price of 18 oranges = Rs 16x
Selling price of 1 orange = Rs 16x/18
By using the formula,
Loss = cost price – selling price
= x – 16x/18
= 2x/18
= Rs x/9
By using the formula,
Loss % = (loss/cost price) × 100
= (x/9)/x × 100
= 100/9
= 11 1/9 %
12. Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its
repairs and sold the motor cycle to Rahul for Rs 35910, thereby making a profit of
12.5%, find the cost price of the motor cycle for Ravish.
Solution:
Let us consider the cost price of motorcycle for Ravish be Rs x
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