The price of diamond varies directly as square of its weight. the price of a 12 decigrams diamond is $7200. if diamond breaks into two pieces whose weights are in the ratio 3: 1, find the loss incurred.

Define price and weight

Let the price of the diamond be y and the weight be x.


General equation for y varies directly as square root of x

y = kx², where k is a constant


Find the constant k

when x = 12,  y = 7200
7200 = k(12)²
7200 = 144k
k = 7200 ÷ 144
k = 50


Substitute k into the equation

y = 50x²


Calculate the weight of the two broken diamonds

The diamond is broken into 3:1
3 + 1 = 4
4 shares = 12

1 share = 12 ÷ 4
1 share = 3 decigrams

3 shares = 3 x 3 
3 shares = 9 decigrams

Ratio 1 : 3 = 3 decigrams : 9 decigrams


Find price of the of the 3 decigrams

y = 50(3)²
y = $450


Find the price of the 9 decigrams

y = 50(9)²
y = $4050


Total price of the 3 decigrams and the 9 decigrams

$450 + $4050 = $4500


Lost incurred

$7200 - $4500 = $2700


The lost incurred is $2700