The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 3 : 4 : 5. When the pieces were sold, the merchant got Rs.59,000 less. Find the original price of the diamond.

84500

According to the ratio 1 : 3: 4 : 5, let total weight of the original diamond = 13 units

Cost of original diamond = 169R

Coat of broken pieces = 1R + 9R + 16R + 25R = 51R

Now, the loss of breakage was (169 - 51)R = ₨. 59000

⇒ 118R = 59000 or 1R = 500

Price of original diamond = 169 x 500 = Rs.84500