Question

the cost of diamond (d) varies directly as the cube of its weight​

Answer 1

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 R