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CAT 2024 Slot 1 — QA Question 8

Profit & LossEasy

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

Answer & solution

  • A

    10

  • 14

  • C

    15

  • D

    20

Solution

Medium

Let the original cost be CC. Write the original selling price as 1.4C1.4C. Then set up the second scenario — cost cut 40%40\%, selling price 55 less, profit 50%50\% — and solve for CC.

1

Original selling price. A 40%40\% profit means

SP=1.40 C\begin{aligned} &\text{SP}=1.40\,C \end{aligned}
2

Second scenario. New cost =0.6C=0.6C; new selling price =1.4C−5=1.4C-5 gives 50%50\% profit on the new cost.

1.4C−5=1.5×(0.6C)⇒ 1.4C−5=0.9C(compute RHS)⇒ 0.5C=5⇒ C=10\begin{aligned} &1.4C-5=1.5\times(0.6C)\\ &\Rightarrow\ 1.4C-5=0.9C \quad\text{(compute RHS)}\\ &\Rightarrow\ 0.5C=5\\ &\Rightarrow\ C=10 \end{aligned}
3

Back to the original selling price using step 1.

SP=1.4×10=14\begin{aligned} &\text{SP}=1.4\times10=14 \end{aligned}
Original SP=Rs 14\text{Original SP}=\text{Rs }14
CAT 2024 Slot 1 QA Q8: The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been so — Solution | TheCATExam