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Faulty Scale Profit Percentage

CAT 1996 Slot 1 · Quantitative Ability · Medium · QA

This is a medium Quantitative Ability question from the CAT 1996 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Instead of a metre scale, a cloth merchant uses a 120 cm120\text{ cm} scale while buying, but uses an 80 cm80\text{ cm} scale while selling the same cloth. If he offers a discount of 20%20\% on cash payment, what is his overall profit percentage?

  1. A.

    20%

  2. B.

    25%

  3. C.

    40%

  4. D.

    15%

Answer

A

Explanation

Cost per true cm bought = 100120=56\frac{100}{120} = \frac{5}{6}. Selling price for 80 cm80\text{ cm} at 20%20\% discount on 100100 = 8080 rs   ⟹  1 rs/cm\implies 1\text{ rs/cm}. Profit %=1−5/65/6×100=20%\% = \frac{1 - 5/6}{5/6} \times 100 = 20\%.

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