Cost of diamond varies directly as the square of its weight. Once, this…
2024
Cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3: 4. When the pieces were sold, merchant got 70000 less. Find the original price of the diamond.
- A.
2.1 lakh
- B.
1.0 lakh
- C.
2.0 lakh
- D.
1.4 lakh
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Show answer & explanation
Correct answer: B
Answer: 1.0 lakh
Let the four piece weights be x, 2x, 3x and 4x. Total weight = 10x.
Since price varies as the square of weight, original price ∝ (10x)^2 = 100·x^2.
Price after breaking = x^2 + (2x)^2 + (3x)^2 + (4x)^2 = 1x^2 + 4x^2 + 9x^2 + 16x^2 = 30·x^2.
Loss = original − sold = 100·x^2 − 30·x^2 = 70·x^2. Given loss = 70000, so 70·x^2 = 70000 ⇒ x^2 = 1000.
Original price = 100·x^2 = 100 × 1000 = 100000 = 1.0 lakh.