Chapter 8 Comparing Quantities Ex 8.3 Solutions
Question - 1 : - Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for ₹ 250 and sold for ₹ 325.
(b) A refrigerator bought for ₹ 12,000 and sold at ₹ 13,500.
(c) A cupboard bought for ₹ 2,500 and sold at ₹ 3,000.
(d) A skirt bought for ₹ 250 and sold at ₹ 150.
Answer - 1 : -
(a) Here, CP = ₹ 250
SP = ₹ 325
Since SP > CP
∴ Profit = SP – CP
= ₹ 325 – ₹ 250 = ₹ 75
Hence, the required profit = ₹ 75
and Profit per cent = 30%
(b) Here, CP = ₹ 12,000
SP = ₹ 13,500
Since SP > CP
∴ Profit = SP – CP
= ₹ 13,500 – ₹ 12,000 = ₹ 1,500
Hence, the required profit = ₹ 1500 × 100
profit % = 
(c) Here, CP = ₹ 2500
SP = ₹ 3000
Since SP > CP
∴ Profit = SP – CP
= ₹ 3000 – ₹ 2500 = ₹ 500
Hence, the required profit = ₹ 500 and profit% = 20%
(d) Here, CP = ₹ 250
SP = ₹ 150
Here CP > SP
∴ Loss = CP – SP
= ₹ 250 – ₹ 150 = ₹ 100
Hence, the required loss = ₹ 100 and loss% = 40%
Question - 2 : - Convert each part of the ratio to Percentage:
(a) 3:1
(b) 2:3:5
(c) 1 : 4
(d) 1:2:5
Answer - 2 : -
(a) 3 : 1
Sum of the ratio parts = 3 + 1 = 4
(b) 2 : 3 : 5
Sum of the ratio parts = 2 + 3 + 5 = 10
(c) 1 : 4
Sum of the ratio parts =1 + 4 = 5
(d) 1 : 2 : 5
Sum of the ratio parts = 1 + 2 + 5 = 8
Question - 3 : - The population of a city decreased from 25,000 to 24,500. Find the Percentage decrease.
Answer - 3 : -
Initial population = 25,000
Decreased population = 24,500
Decrease in population
= 25,000 – 24,500 = 500
Percentage of decrease = 
= 2% Hence the Percentage of decrease in population = 2%.
Question - 4 : - Arun bought a car for ₹ 3,50,000. The next year, the price went upto ₹ 3,70,000. What was the Percentage of price increase?
Answer - 4 : -
Original price of the car = ₹ 3,50,000
Price increased next year = ₹ 3,70,000
Increase in price = ₹ 3,70,000 – ₹ 3,50,000
= ₹ 20,000
∴ Percentage of the increase in the price
Hence, the Percentage of increase in price = 
Question - 5 : - I buy a TV for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it?
Answer - 5 : -
Here, CP = ₹ 10,000
Profit = 20%
SP = ?
Hence, the required money got by me = ₹ 12,000.
Question - 6 : - Juhi sells a washing machine for ₹ 13,500. She loses 20% in the bargain. What was the price at which she bought it?
Answer - 6 : -
SP of the washing machine = ₹ 13,500
Loss = 20%
CP = ?
Hence, the cost price of the machine = ₹ 16875.
Question - 7 : - (i) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the Percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?
Answer - 7 : -
(i) Sum of the ratio parts = 10 + 3 + 12 = 25
∴ Percentage of carbon in chalk
Hence, the Percentage of carbon in chalk = 12%
(ii) Weight of carbon = 3 g
∴ Weight of chalk = =3/3 × 25 g = 25 g
Hence, the weight of chalk = 25 g
Question - 8 : - Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?
Answer - 8 : -
CP of book = ₹ 275
Loss = 15%
Hence, the required selling price = ₹ 233.75
Question - 9 : - Find the amount to be paid at the end of 3 years in each case.
(a) Principal = ₹ 1200 at 12% p.a.
(b) Principal = ₹ 7500 at 5% p.a.
Answer - 9 : -
(a) Given: Principal = ₹ 1200
Rate of interest = 12% p.a., T = 3 years
∴ Interest = 
Amount = Principal + Interest
= ₹ 1200 + ₹ 432 = ₹ 1632
Hence, the required amount = ₹ 1632
(b) Given: Principal = ₹ 7500
Rate = 5% p.a.
Time = 3 years
∴ Interest =
= ₹1125
Amount = Principal + Interest
= ₹ 7500 + 11125 = ₹ 8625
Hence, the required amount = ₹ 8625.
Question - 10 : - What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?
Answer - 10 : -
Given: Principal = ₹ 56,000
Interest = ₹280
Time = 2 years
Rate = ?
Hence, the required rate = 0.25%