CAT 2024 Slot 1 · Quant · Question 21
CAT 2024 Slot 1 previous year question on Profit and Loss, with the answer and a step-by-step solution.
- A10
- B15
- C20
- D14
Answer & solution
Answer: Option D
Let the cost price be x.
A 40% profit fixes the selling price at 1.4x.
In the alternative scenario the cost falls by 40%, so it becomes 0.6x.
The selling price there is 5 less than before, that is 1.4x-5.
A 50% profit on the reduced cost means the selling price is 1.5\times 0.6x=0.9x.
Equating the two expressions, 1.4x-5=0.9x.
So 0.5x=5 and x=10.
The original selling price is 1.4\times 10=14.
Shortcut. Notice that 1.5\times 0.6=0.9, so the hypothetical selling price is just 0.9x. The whole question is then the single equation 1.4x-0.9x=5, giving the cost in one step.
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