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?

₹62,400

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.