Profit and Loss Question 2 - CAT 2025
An item with a cost price of Rs. 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 Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to:
Step-by-Step Explanation
Let the marked price be M and the initial discount rate be d.
- Initial Scenario (20% Profit):
Initial SP = 1650 × 1.20 = 1980
M(1 − d) = 1980 --- (Equation 1)
- Second Scenario (Discount Doubled):
The new profit is Rs. 110.
New SP = CP + Profit = 1650 + 110 = 1760
M(1 − 2d) = 1760 --- (Equation 2)
Subtracting Equation 2 from Equation 1:
M(1 − d) − M(1 − 2d) = 1980 − 1760
Md = 220
Substitute Md = 220 into Equation 1:
M − Md = 1980
M − 220 = 1980
M = 2200
Since M = 2200, we find d:
2200 × d = 220
d = 0.10 (or 10%)
- Final Scenario (Profit % = Discount %):
Let the new discount rate be r. The new selling price will be 2200(1 − r).
We are given that:
Profit % = r
(SP − CP) / CP = r
[2200(1 − r) − 1650] / 1650 = r
2200 − 2200r − 1650 = 1650r
550 = 3850r
r = 550 / 3850 = 1 / 7 ≈ 0.142857
Expressed as a percentage, r ≈ 14.28%, which is nearest to 14.
Correct Option: C
💡 FundaMakers Tip:
Look for the linear relationship! When the discount rate doubles from d to 2d, the absolute value of the discount increases by exactly Md. Consequently, the Selling Price drops by exactly Md.
Drop in SP = 1980 − 1760 = 220
You can instantly write Md = 220 without setting up tedious equations. Spotting these variations helps you crack CAT Quant questions in under a minute.