The value of diamond is directly proportional to the square of its weight.

Ques - The value of diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into 3 pieces with weights in ratio 3 : 4 : 5, thus a loss of Rs. 9.4 lakh is incurred. What is the actual value of diamond?

(a) 28.8 lakh

(b) 13.5 lakh

(c) 14.4 lakh 

(d) 18.8 lakh

Solution - 

It is given that the value of the diamond is directly proportional to the square of its weight.

Value of Diamond = (weight)²

Also,

It is given that the diamond gets broken into 3 pieces in the ratio of 3 : 4 : 5.

Let,

The weight of the broken pieces be in the ratio of = 3x : 4x : 5x

The total weight of the diamond = 3x + 4x + 5x

= 12x

So,

Value of Diamond = (weight)²

Value of Diamond = (12x)²

Value of Diamond = 144x²

The total value of 3 broken pieces = (3x)² + (4x)² + (5x)²

= 9x² + 16x² + 25x²

= 50x²

A loss of Rs. 9.4 lakh is incurred 

we can say,

144x² - 9,40,000 = 50x²

144x² - 50x² = 9,40,000

94x² = 9,40,000

x² = 9,40,000 / 94

x² = 10,000

The actual value of diamond = 144x²

The actual value of diamond = 144 x 10,000

The actual value of diamond = 14,40,000

The actual value of diamond = 14.4 lakh

Hence,

The correct answer is option (c) 14.4 lakh.

Thank You