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

Let rate of depreciation be r%.

Depreciation formula,

V = $V_0\Big(1 - \dfrac{r}{100}\Big)^n$

Putting values in formula we get,

$\Rightarrow 14440 = 16000\Big(1 - \dfrac{r}{100}\Big)^2 \\[1em] \dfrac{14440}{16000} = \Big(1 - \dfrac{r}{100}\Big)^2 \\[1em] \dfrac{1444}{1600} = \Big(1 - \dfrac{r}{100}\Big)^2 \\[1em] \Big(\dfrac{38}{40}\Big)^2 = \Big(1 - \dfrac{r}{100}\Big)^2 \\[1em] 1 - \dfrac{r}{100} = \dfrac{38}{40} \\[1em] \dfrac{r}{100} = 1 - \dfrac{38}{40} \\[1em] \dfrac{r}{100} = \dfrac{2}{40} \\[1em] r = \dfrac{200}{40} \\[1em] r = 5\%.$

Hence, the rate of depreciation = 5%.