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Proportional Cost of Diamond

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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The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:41 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.

  1. A.

    Rs. 1.4 lakh

  2. B.

    Rs. 2 lakh

  3. C.

    Rs. 1 lakh

  4. D.

    Rs. 2.1 lakh

Answer

C

Explanation

Total weight = 1+2+3+4=10x1 + 2 + 3 + 4 = 10x. Original cost ∝(10x)2=100x2\propto (10x)^2 = 100x^2. Broken cost ∝(12+22+32+42)x2=30x2\propto (1^2 + 2^2 + 3^2 + 4^2)x^2 = 30x^2. Loss =70x2=70,000  ⟹  x2=1,000= 70x^2 = 70,000 \implies x^2 = 1,000. Original price =100×1,000=1,000,000=Rs. 1 lakh= 100 \times 1,000 = 1,000,000 = \text{Rs. 1 lakh}.

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