NCERT Solutions: Comparing Quantities (Old Questions)

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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
= (5/100) × Rs 750
= (5 × 750) / 100 = Rs 3,750 / 100 = 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 1,200
∴ Profit = 5% of Rs 1,200
= (5/100) × Rs 1,200
= (5 × 1,200) / 100 = Rs 6,000 / 100 = Rs 60
Now, SP = CP + Profit
= Rs 1,200 + Rs 60
= Rs 1,260

(c) ∵ Total cost price = Rs 560 + Rs 40 (Overhead expenses)= Rs 600

∴ Profit = 5% of Rs 600
= (5/100) × Rs 600
= (5 × 600) / 100 = Rs 3,000 / 100 = 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 TVs = 2 × Rs 10,000
= Rs 20,000
For 1st TV: CP = Rs 10,000
Profit rate = 10%
∴ Profit = 10% of Rs 10,000
= (10/100) × Rs 10,000 = Rs 1,000

∴ SP of 1st TV = Rs 10,000 + Rs 1,000 = 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 1,000
∴ SP of 2nd TV = Rs 10,000 - Rs 1,000 = Rs 9,000
Now, Total SP of both the TVs = Rs 11,000 + Rs 9,000
= Rs 20,000
∵ Total cost price = Total 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
= (5/100) × Rs 50 = Rs 250 / 100 = Rs 2.50
Thus, the buying price of the towel = Rs 50 + Rs 2.50
= Rs 52.50

(b) ∵ Cost of the two soap bars = (Rs 35) × 2 = Rs 70
∴ Sales tax = 5% of Rs 70
= (5/100) × Rs 70 = Rs 350 / 100 = Rs 3.50
Thus, the buying price = Rs 70 + Rs 3.50
= Rs 73.50

(c) ∵ Cost of 5 kg of flour = Rs 15 × 5 = Rs 75
∴ Sales tax = 5% of Rs 75
= (5/100) × Rs 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 13,500
Rate of VAT = 8%
Let the original price = Rs x
∴ x + 8% of x = Rs 13,500
or x (1 + 8/100) = Rs 13,500
or x × 108/100 = Rs 13,500

∴ x = Rs 13,500 × 100 / 108 = Rs 13,500 ÷ 1.08 = Rs 12,500
Thus, the original price = Rs 12,500. 

(b) Let original price = Rs x

∴ Price including VAT = x + 8% of x = x × 108/100

But the price including VAT = Rs 180

∴ x × 108/100 = Rs 180
or x = Rs 180 × 100 / 108

or x = Rs 180 × 25 / 27 = Rs 4,500 / 27 = Rs 166.66

Thus, the original price = Rs 166.66