Question

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.

• A. ₹55625
• B. ₹43175
• C. ₹49352
• D. ₹50625

Answer 1

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 $V_0$

$\text{Using depreciation formula,}V=V_0{(1-\frac{r}{100})}^n$
$\Rightarrow 35600=V_0{(1-\frac{20}{100})}^2\Rightarrow 35600=V_0{\left(\frac{80}{100}\right)}^2=V_0\left(\frac{16}{25}\right)\Rightarrow V_0=35600\times \frac{25}{16}=₹55625$