A manufacturer estimates that his machine depreciates by 15% of its value at the beginning of the year. Find the original value of machine, if it depreciates by ₹ 5355 during the second year.

Let original value of machine be ₹ x.

For first year :

P = ₹ x

R (of depreciation) = 15%

T = 1 year

Depreciation = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 15 \times 1}{100} = \dfrac{3x}{20}$.

New value = P - Depreciation = $x - \dfrac{3x}{20} = \dfrac{17x}{20}$.

For second year :

P = ₹ $\dfrac{17x}{20}$

R (of depreciation) = 15%

T = 1 year

Depreciation = $\dfrac{P \times R \times T}{100} = \dfrac{\dfrac{17x}{20} \times 15 \times 1}{100} = \dfrac{51x}{400}$.

Given,

Depreciation in second year = ₹ 5355

$\therefore \dfrac{51x}{400} = 5355 \\[1em] \Rightarrow x = \dfrac{5355 \times 400}{51} \\[1em] \Rightarrow x = 105 \times 400 = 42000.$

Hence, original value of machine = ₹ 42000.