The cost of diamond varies directly as the square of its weight. A diamond weight $10$ grams cost $R s 8, 000$ . If it breaks into two pieces whose weights are in the ratio $3 : 2$ , then the loss incurred (in rupees)

3840

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3960

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4040

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4160

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Solution

The correct option is A $3840$
Cost of diamond $= k (w e i g h t)^{2}$
$8000 = k (10)^{2}$
$k = \frac{8000}{100} = 80$
Diamond was broke into two pieces = $3 x + 2 x = 10$ ,
$5 x = 10 \Rightarrow x = 2$
Ist part: $3 x = 6$
IInd part: $2 x = 4$
Ist part; $c o s t \Rightarrow 80 \times 36 = 2880$
IInd part; $c o s t \Rightarrow 80 \times 16 = 1280$
Total cost = $2880 + 1280 = 4160$
So loss = $8000 - 4160 = 3840$

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The cost of diamond varies directly as the square of its weight. A diamond weight 10 grams cost Rs8,000. If it breaks into two pieces whose weights are in the ratio 3:2, then the loss incurred (in rupees)

The correct option is A 3840Cost of diamond =k(weight)2 8000=k(10)2k=8000100=80Diamond was broke into two pieces = 3x+2x=10, 5x=10⇒x=2Ist part: 3x=6 IInd part: 2x=4Ist part; cost⇒80×36=2880IInd part; cost⇒80×16=1280Total cost = 2880+1280=4160So loss = 8000−4160=3840

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