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Question

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs Rs. 8,000. If it breaks into two pieces whose weights are in the ratio 3 : 2, then the loss incurred (in rupees) is ___.


A
3840
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B
3960
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C
4040
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D
4160
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Solution

The correct option is A 3840

Let C denote cost and W denote weight
Cw2
C=kw2 (k = constant)
8000=k(10)2
k =80
10 dgm dividing in 3 : 2 we get 6 dgm : 4 dgrm.
C1=80(6)2=80×36=Rs.2880
C2=80(4)2=80×16=Rs.1280C1+C2=2880+1280=Rs.4160

Loss = 8000 - 4160 = Rs. 3840


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