The cost of a bike, purchased 2 years ago, depreciates at the rate of $20 %$ every year. If its present worth is ₹35600, find its purchase price.

₹55625

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₹43175

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₹49352

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₹50625

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Solution

The correct option is A
₹55625

Let the present value of the car be $V$ which is ₹35600.
Time, $n = 2$ years, and rate of depreciation, $r = 20 %$ per annum.

Let the purchase price be $V_{0}$

$Using depreciation formula, V = V_{0} {(1 - \frac{r}{100})}^{n}$
$\Rightarrow 35600 = V_{0} {(1 - \frac{20}{100})}^{2} \Rightarrow 35600 = V_{0} {(\frac{80}{100})}^{2} = V_{0} (\frac{16}{25}) \Rightarrow V_{0} = 35600 \times \frac{25}{16} = ₹ 55625$

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The cost of a bike, purchased 2 years ago, depreciates at the rate of 20% every year. If its present worth is ₹35600, find its purchase price.

The cost of a bike, purchased 2 years ago, depreciates at the rate of $20 %$ every year. If its present worth is ₹35600, find its purchase price.