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The cost of diamond varies directly as the cube of its weight. Once this diamond broke into 4 pieces with weights in the ratio 3 : 2 : 1 : 1. When the pieces were sold the merchant got 30600 less. Find the original price of the diamond?

The cost of diamond varies directly as the cube of its weight. Once this diamond broke into 4 pieces with weights in the ratio 3 : 2 : 1 : 1. When the pieces were sold the merchant got 30600 less. Find the original price of the diamond? Correct Answer Rs. 34300

Given:

Ratio of diamond when broke is 3 : 2 : 1 : 1.

When the pieces were sold the merchant got 34600 less.

Concept used:

Using the concept simple ratio.

Calculation:

Let the weight of each piece of diamond be 3x, 2x, x and x.

Total weight of diamond = 3x + 2x + x + x = 7x  

Cost of the diamond = (7x)3 = 343x3

Cost of first piece = (3x)3 = 27x3

Cost of second piece = (2x)3 = 8x3

Cost of third piece = (x)3 = x3

Cost of fourth piece = (x)3 = x3

Total cost of diamond after weight = 27x3 + 8x3 + x3 + x3

⇒ New cost = 37x3

According to the question,

343x3 – 37x3 = 30600

⇒ 306x3 = 30600

⇒ x3 = 100

So, the original cost of diamond = 343x3 = 343 × 100 = Rs. 34300

∴ The original cost of diamond is Rs. 34300.

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