The value of a machine worth ₹500000 is depreciating at the rate of 10% every year. In how many years will its value be reduced to ₹364500?

Let value be depreciated from ₹500000 to ₹364500 in n years.

Depreciation formula,

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

Putting values in formula we get,

$\Rightarrow 364500 = 500000\Big(1 - \dfrac{10}{100}\Big)^n \\[1em] \Rightarrow \dfrac{364500}{500000} = \Big(\dfrac{100 - 10}{100}\Big)^n \\[1em] \Rightarrow \dfrac{729}{1000} = \Big(\dfrac{90}{100}\Big)^n \\[1em] \Rightarrow \Big(\dfrac{9}{10}\Big)^3 = \Big(\dfrac{9}{10}\Big)^n \\[1em] \therefore n = 3.$

Hence, the value of machine will be depreciated from ₹500000 to ₹364500 in 3 years.