Question
Download Solution PDFPrice of a diamond is directly proportional to square of its weight. A man broke the diamond accidently in three pieces. The ratio of weights of these three pieces is 4 : 3 : 2. He loses Rs. 18720, What was the original price of the diamond?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Price ∝ (Weight)2
Weight ratio = 4 : 3 : 2
Loss = ₹18720
Calculation:
If weights = 4x, 3x, 2x
Original price ∝ (4x + 3x + 2x)2 = (9x)2 = 81x2
New price = (4x)2 + (3x)2 + (2x)2 = 16x2 + 9x2 + 4x2 = 29x2
Loss = Original - New = 81x2 - 29x2 = 52x2
52x2 = 18720
⇒ x2 = 18720 / 52 = 360
⇒ Original price = 81x2 = 81 × 360 = ₹29160
∴ Original price of the diamond = ₹29160
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