Question 8

# A granite stone has been purchased to build the kitchen platform and dining area of Mr. Kumar's bungalow. The cost of the stone varies directly with square of its weight. The stone broke into four parts whose weights are in the ratio of 2:4:7:11. If the granite stone had broken into four equal parts of weight then it would have led to a loss of Rs. 73600. What is the actual cost of the original granite stone (unbroken)?

Solution

It is given,
cost(c) is directly proportional to square of weight ($$w^2$$), i.e.
$$c=k.w^2$$
Cost when block is divided into four parts whose weights are in ratio 2:4:7:11
Let the weights be 2x, 4x, 7x, 11x
Cost = k ($$4x^2+16x^2+49x^2+121x^2$$) = $$190kx^2$$
Cost when block is divided into four equal parts
Let the weights be 6x, 6x, 6x, 6x
Cost = k ($$4*36x^2$$) = $$144kx^2$$
It is given,
$$190kx^2-144kx^2 = 73600$$
$$kx^2= 1600$$
Actual weight of granite = 24x
Cost = $$576kx^2$$ = 576*1600 = 921600
The answer is option C.