Question

The cost of the plyboard varies directly with square of its weight. Plyboard is broken into 3 parts whose weight are in the ratio 9 : 2 : 1. If plyboard had been broken into three part whose weight are in the ratio 7 : 3 : 2 then there would have been a further loss of Rs. 448. What is the actual cost of original plyboard?

Answer 1

Given:

The cost of the ply board varies directly with square of its weight.

To find:

The cost of the ply board.

Solution:

1)  In the first case the ply board is broken in 3 parts in ratio of its weight is 9:2:1.

So the ratio of its cost will be:

• 9²:2²:1²

• 81:4:1

Total cost will be 86

2) And in second case the ply board is again broken into 3 parts in ratio of its weight is 7:3:2.

So the ratio of its cost will be:

• 7²:3²:2²

• 49:9:4

Total cost in this case will be 62.

3) Cost of the original ply board is (9+2+1)² or (7+3+2)² = 12² = 144

4) According to the question the loss is 86-62 = 24

and ₹448 is given in the question

so,

• 24 ------ 448

• 1    ------- 448/24

• 144 ------(448/24)×144

•              ₹ 2688

The cost of the original ply board is ₹2688.