The value of a machine depreciates at the rate of $16\dfrac{2}{3}\%$ per annum. It was purchased 3 years ago. If its present value is ₹ 62,500, find its purchase price.

Given,

Present value of machine (V) = ₹ 62,500

R = $16\dfrac{2}{3} = \dfrac{48 + 2}{3} = \dfrac{50}{3}\%$

n = 3 years

By formula,

Value of machine n years ago = ₹ $\dfrac{V}{\Big(1 - \dfrac{r}{100}\Big)^n}$

Substituting the values in formula,

$\text{Value of machine 3 years ago}=\dfrac{62500}{\Big(1 - \dfrac{\dfrac{50}{3}}{100}\Big)^3} \\[1em] =\dfrac{62500}{\Big(1 - \dfrac{50}{3 \times 100}\Big)^3} \\[1em] =\dfrac{62500}{\Big(\dfrac{300 - 50}{300}\Big)^3} \\[1em] =\dfrac{62500}{\Big(\dfrac{250}{300}\Big)^3} \\[1em] =\dfrac{62500}{\Big(\dfrac{25}{30}\Big)^3} \\[1em] =\dfrac{62500}{\dfrac{15625}{27000}} \\[1em] =\dfrac{62500 \times 27000}{15625} \\[1em] =₹ 1,08,000$

Hence, its purchase price = ₹ 1,08,000.