The value of a stone is proportional to the square of its weight. A stone worth ₹1,20,000 is broken into two pieces in the ratio of 2 : 3. What is the total price of the two small stones?
Answer & explanation
Correct answer: option 2
Let's suppose, the weights of the small pieces 2k and 3k units.
Initial total weight of the stone = 3k + 2k = 5k units.
According to the question,
⇒ (5k)2 α 120000
⇒ (25k)2 x F = 120000 (F = constant)
⇒ k2 F = 4800 ..(1.)
⇒ Value of 2k stone
⇒ \( {2k }^{2 } \) x F = \( {2k }^{2 } \) x F
⇒ 4 x 4800 (from 1)
⇒ Rs. 19200
The value of 3k stone
⇒ \( {3k }^{2 } \) x F = \( {9k }^{2 } \) x F
⇒ 9 x 4800
⇒ Rs. 43200
Now, the total price of the two small stones = 43200 + 19200 = Rs. 62,400.