NCERT Solutions for Class 8 Maths - Comparing Quantities (Old Questions)

Try These

Question 1. Find selling price (SP) if a profit of 5% is made on

(a) a cycle of Rs 700 with Rs 50 as overhead charge.

(b) a lawn mower bought at Rs 1150 with Rs 50 as transportation charges.

(c) a fan bought for Rs 560 and expenses of Rs 40 made on its repairs.

Solution:

(a) ∵ Total cost price = Rs 700 + Rs 50 (Overhead expenses)

= Rs 750

Profit = 5% of Rs 750

= Rs 5/100 * Rs 750 = Rs 5 * 15/2

= Rs 75/2 = Rs 37.50

Now, SP = CP + Profit

= Rs 750 + Rs 37.50

= Rs 787.50

(b) ∵ Total cost price = Rs 1150 + Rs 50 (Overhead expenses)

= Rs 1200

∴ Profit = 5% of Rs 1200

= 5/100 * Rs 1200

= Rs 5 * 12 = Rs 60

Now, SP = CP + Profit

= Rs 1200 + Rs 60

= Rs 1260

(c) ∵ Total cost price = Rs 560 + Rs 40 (Overhead expenses)

= Rs 600

∴ Profit = 5% of Rs 600

= 5/100 * Rs 600

= Rs 5 * 6 = Rs 30

Now, SP = CP + Profit

= Rs 600 + Rs 30

= Rs 630

Question 2. A shopkeeper bought two TV sets at Rs 10,000 each. He sold one at a profit 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.

Solution: Total CP of both TV’s = 2 x Rs 10,000

= Rs 20,000

For 1st TV: CP = Rs 10,000.

Profit rate = 10%

∴ Profit = 10% or Rs 10,000

= 10/100 * Rs 10,000 = Rs 1000

∴ SP = Rs 10,000 + Rs 1000 = Rs 11,000

For 2nd TV: CP = Rs 10,000

Loss rate = 10%

∴ Loss = 10% of Rs 10,000

= 10/100 * Rs 10,000 = Rs 1000

∴ SP = CP – Loss

= Rs 10,000 – Rs 1000 = Rs 9000

Now, Total SP of both the TV’s = Rs 11,000 + Rs 9000

= Rs 20,000

∵ Cost price = Selling price

∴ There is no overall profit or loss.

Question 3. Find the buying price of each of the following when 5% ST is added on the purchase of 

(a) A towel at Rs 50

(b) Two bars of soap at Rs 35 each

(c) 5 kg of flour at Rs 15 per kg

Solution:

(a) Cost of the towel = Rs 50

∴ Sales tax on the towel = 5% of Rs 50

= Rs 5/100 * 50 = Rs 2.5

Thus, the buying price of the towel = Rs 50 + Rs 2.5

= Rs 52.5

(b) ∵ Cost of the two soap bars = (Rs 35) * 2 = Rs 70

∴ Sales tax = 5% of Rs 70

= Rs 5/100 * 70 = Rs 3.5

Thus, the buying price = Rs 70 + Rs 3.5

= Rs 73.5

(c) ∵ Cost of 5 kg of flour = Rs 15 * 5 = Rs 75

∴ Sales tax = 5% of Rs 75

= Rs 5/100 * 75 

= Rs 375/100 = Rs 3.75

Thus, the buying price = Rs 75 + Rs 3.75

= Rs 78.75

Question 4. If 8% VAT is included in the prices, find the original price of

(a) A TV bought for Rs 13,500  (b) A shampoo bottle bought for Rs 180 

Solution:

(a) Cost of TV including VAT = Rs 13500

Rate of VAT = 8%

Let the original price = Rs x

∴  x + 8% of x = Rs 13,500

or  x + 8/100 x =  Rs 13500

or  

or  

or 

Thus, the original price = Rs 12500. 

(b) Let original price = Rs x

∴ Price including VAT = Rs x + 8% of x

But the original price + VAT = Rs 180

∴  

or  

Thus, the original price = Rs 166 2/3