CAT 2025 Slot 2 · Quant · Question 15

CAT 2025 Slot 2 previous year question on Profit and Loss, with the answer and a step-by-step solution.

Profit and LossArithmeticMultiple choiceMedium

An item with a cost price of ₹1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been ₹110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to

A
12
B
14
C
16
D
18

Pick an option, then check.

Answer & solution

Answer: Option B

A 20% profit on 1650 gives a selling price of 1650\times 1.2=1980.

A profit of 110 gives a selling price of 1650+110=1760.

Writing M for the marked price and D for the first discount in rupees, M-D=1980 and M-2D=1760.

Subtracting the second from the first, D=1980-1760=220.

So M=1980+220=2200.

If the required discount rate is d\%, the selling price is 2200\left( 1-\frac{d}{100}\right), and since the profit percentage must also be d, it equals 1650\left( 1+\frac{d}{100}\right).

Equating and expanding, 2200-22d=1650+16.5d.

So 550=38.5d and d=\frac{550}{38.5}=14.28\ldots, nearest to 14.

Shortcut. Doubling a discount cuts the selling price by exactly one more discount, so the discount in rupees is just the drop in selling price: 1980-1760=220. That gives M=2200 in two subtractions, with no equations.

CAT 2025 Slot 2 · Quant · Question 15

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