CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
The cost of a diamond varies as the square of its weight. A diamond weighing 6 carats is broken into two pieces with weights in the ratio 1 : 2 and its total value falls by ₹16,000. What was the original value of the diamond?
The original value was ₹36,000. Value is k times weight squared, so the whole stone is 36k and the pieces of 2 and 4 carats are 4k and 16k. The loss is 16k = ₹16,000, so k = 1,000 and 36k = ₹36,000.
- A₹36,000
- B₹28,800
- C₹32,400Correct
- D₹30,000
Explanation
Value = k w². Original = 36k. Pieces weigh 2 and 4, giving k(4 + 16) = 20k. Loss = 36k − 20k = 16k = 16,000, so k = 1,000. Original value = 36 × 1,000 = ₹36,000. Check: pieces worth 20,000, loss 16,000. So the correct value is ₹36,000, not ₹32,400.
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