The cost of diamond varies directly as the square of its weight. A diamond weighing10 decigrams cost Rs. 8,000. If it breaks into two pieces whose weights are in the ratio 3: 2, then the loss incurred (in rupees) is

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

Let C denote cost and W denote weight
$∴ C \propto w^{2}$
$C = k w^{2}$ (k = constant)
$\Rightarrow 8000 = k (10)^{2}$
$\Rightarrow$ k =80
10 dgm dividing in 3 : 2 we get 6 dgm : 4 dgrm.
$C_{1} = 80 (6)^{2} = 80 \times 36 = R s . 2880$
$C_{2} = 80 (4)^{2} = 80 \times 16 = R s . 1280 C_{1} + C_{2} = 2880 + 1280 = R s . 4160$

Loss = 8000 - 4160 = Rs. 3840

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The cost of diamond varies directly as the square of its weight. A diamond weighing10 decigrams cost Rs. 8,000. If it breaks into two pieces whose weights are in the ratio 3: 2, then the loss incurred (in rupees) is

The correct option is A 3840 Let C denote cost and W denote weight ∴C∝w2 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