During every financial year, the value of a machine depreciates by 12%. Find the original cost of a machine which depreciates by ₹ 2640 during the second financial year of its purchase.

Let original value of machine be ₹ x.

For first year :

P = ₹ x

R (of depreciation) = 12%

T = 1 year

Depreciation = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 12 \times 1}{100} = \dfrac{12x}{100}$

Value at end of first year = P - Depreciation = $x - \dfrac{12x}{100} = \dfrac{88x}{100}$.

For second year :

P = $\dfrac{88x}{100}$

R (of depreciation) = 12%

T = 1 year

Depreciation = $\dfrac{P \times R \times T}{100} = \dfrac{\dfrac{88x}{100} \times 12 \times 1}{100} = \dfrac{1056x}{10000}$

Given,

Machine depreciates by ₹ 2640 during the second financial year of its purchase.

$\therefore \dfrac{1056x}{10000} = 2640 \\[1em] \Rightarrow x = \dfrac{2640}{1056} \times 10000 \\[1em] \Rightarrow x = 2.5 \times 10000 \\[1em] \Rightarrow x = 25000.$

Hence, original cost of machine = ₹ 25000.