A precious crystal piece worth Rs. 15600 is accidentally dropped and was Brocken into three piece, their weights respectively proportional to 2, 3 and 5 units. Value of the crystal varies directly as the cube of its weight. Calculate the percentage loss in the value.
Answers
Given : crystal piece worth Rs. 15600 is accidentally dropped and was Brocken into three piece, their weights respectively proportional to 2, 3 and 5 units. Value of the crystal varies directly as the cube of its weight.
To find : the percentage loss in the value.
Solution:
Let say weight of Crystal = 10 W units
price ∝ (10W)³
Price = k (10W)³
= 1000 kW ³
Broken into three piece, their weights respectively proportional to 2, 3 and 5 units
their weight 2W , 3W & 5W
Price = k (2W)³ + k (3W)³ + k (5W)³
= kW³( 8 + 27 + 125)
= kW³(160)
Loss = 1000 kW ³ - 160kW³ = 840kW³
% loss = (840kW³/1000 kW ³) * 100 = 84 %
84 % loss in value
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