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Price of a diamond is directly proportional to square of its weight. A man broke the diamond accidently in three pieces in the ratio of 3 : 5 : 7 and thus loses Rs 42600. What was the original price (in Rs) of the diamond?

Price of a diamond is directly proportional to square of its weight. A man broke the diamond accidently in three pieces in the ratio of 3 : 5 : 7 and thus loses Rs 42600. What was the original price (in Rs) of the diamond? Correct Answer 67500

Let total weight of the diamond is 15 gm.

So, Original price of the diamond = k × 152 = Rs. 225k

Diamond is broken into 3 parts in the ratio of 3 : 5 : 7

Therefore weights of the pieces are 3 gm, 5 gm and 7 gm respectively

Let value of the pieces be Rs. 9k, Rs. 25k, Rs. 49k respectively

According to the question,

225k – = 42600

⇒ 142k = 42600

⇒ k = 42600/142 = 300

∴ Original price of the diamond = 225k = 225 × 300 = Rs. 67500

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