Question

Afridi purchased an old scooter for $Rs.16000$. If the cost of scooter after $2$ years depreciates to $Rs.14440$, find the rate of depreciation.

Answer 1

Current cost of the scooter, $C_o=16000$

Cost after two years, $C=14440$

Let the rate of depreciation be R, then

$C=C_o{(1-\frac{R}{100})}^T$

$\Rightarrow 14400=16000{(1-\frac{R}{100})}^2$

$\Rightarrow \frac{14400}{16000}={(1-\frac{R}{100})}^2$

$\Rightarrow {\left(\frac{38}{40}\right)}^2={(1-\frac{R}{100})}^2$

$\Rightarrow \frac{38}{40}=1-\frac{R}{100}$

$\Rightarrow \frac{R}{100}=1-\frac{38}{40}$

$\Rightarrow R=\frac{2\times 100}{40}$

$\Rightarrow R=5\%$