The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is ₹ 97200, find :

(i) its value after 2 years.

(ii) its value when it was purchased.

(i) In depreciation :

Value after n years = Present value $\times \Big(1 - \dfrac{r}{100}\Big)^n$

$\text{Value of machine after 2 years} = 97200 \times \Big(1 - \dfrac{10}{100}\Big)^2 \\[1em] = 97200 \times \Big(\dfrac{90}{100}\Big)^2 \\[1em] = 97200 \times \Big(\dfrac{9}{10}\Big)^2 \\[1em] = 97200 \times \dfrac{81}{100} \\[1em] = 972 \times 81 \\[1em] = ₹ 78732.$

Hence, value of machine after 2 years = ₹ 78732.

(ii) Let value of machine when it was purchased be ₹ x and its depreciate to ₹ 97200 in two years.

$\therefore 97200 = x \times \Big(1 - \dfrac{10}{100}\Big)^2 \\[1em] \Rightarrow 97200 = x \times \Big(\dfrac{90}{100}\Big)^2 \\[1em] \Rightarrow 97200 = x \times \Big(\dfrac{9}{10}\Big)^2 \\[1em] \Rightarrow 97200 = x \times \dfrac{81}{100} \\[1em] \Rightarrow x = \dfrac{97200 \times 100}{81} \\[1em] \Rightarrow x = 120000.$

Hence, machine's value when it was purchased = ₹ 120000.