Question

Mr Rajveer purchased a unique diamond
called "Zoinoor", which was very
expensive and the cost of the diamond is
proportional to square of its weight. But
he accidently broke the diamond and it
was split into three pieces which were in
ratio of 3:2:1 by weight. If he incurred a
total loss of Rs 46200 due to the
accident, find the initial cost of diamond.​

Answer 1

Given :- The cost of the diamond is proportional to square of its weight. But he accidently broke the diamond and it was split into three pieces which were in ratio of 3:2:1 by weight.

To Find :- If he incurred a total loss of Rs 46200 due to the

accident, find the initial cost of diamond. ?

Answer :-

given that,

→ cost of diamond ∝ (weight)²

→ cost of diamond = (weight)²

now, let us assume that, the diamond was split into 3x , 2x and x by weights .

so,

→ Total weight = 3x + 2x + x = 6x .

then,

→ cost of diamond = (6x)² = 36x² .

also, after breaking,

→ Total weight becomes = x²[(3x)² + (2)² + (1)²] = x²(9 + 4 + 1) = 14x² .

then,

→ Total loss = Rs.46200

→ 36x² - 14x² = 46200

→ 22x² = 46200

→ x² = 2100

therefore,

→ initial cost of diamond = 36x² = 36 * 2100 = Rs.75,600 (Ans.)

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