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CAT 2024 Set-1 | Quantitative Aptitude | Question: 13

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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

  1. $5$
  2. $20$
  3. $10$
  4. $14$

1 Answer

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Given the profit is 40%, so:

Original SP=1.4C\text{Original SP} = 1.4COriginal SP=1.4C

Apply the modified condition

  • New Cost Price = 0.6C0.6C0.6C (because cost is 40% less → C−0.4C=0.6CC - 0.4C = 0.6CC−0.4C=0.6C)

  • New Selling Price = 1.4C−51.4C - 51.4C−5

Profit in the modified case = 50%, so:

1.4C−5=1.5(0.6C)1.4C - 5 = 1.5(0.6C)1.4C−5=1.5(0.6C) 1.4C−5=0.9C1.4C - 5 = 0.9C1.4C−5=0.9C

Subtract 0.9C0.9C0.9C from both sides:

0.5C−5=00.5C - 5 = 00.5C−5=0 0.5C=50.5C = 50.5C=5 C=10C = 10C=10

Now calculate the original selling price

SP=1.4C=1.4×10=14SP = 1.4C = 1.4 \times 10 = 14SP=1.4C=1.4×10=14

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