The cost of a machine depreciated by ₹ 4000 during the first year and by ₹ 3600 during the second year. Calculate :

(i) the rate of depreciation.

(ii) the original cost of the machine.

(iii) its cost at the end of third year.

(i) Difference between depreciation in value between the first and second years is ₹ 4,000 - ₹ 3,600 = ₹ 400

So, the depreciation of one year on ₹ 4,000 = ₹ 400

By formula,

Rate of depreciation = $\dfrac{100 \times I}{P \times T} = \dfrac{100 \times 400}{4000 \times 1}$ = 10%.

Hence, rate of depreciation = 10%.

(ii) Let cost of machine be ₹ x.

Given,

Depreciation in first year = ₹ 4000

Depreciation % = 10%

$\therefore \dfrac{x \times 1\times 10}{100} = 4000$

x = 40000.

Hence, original cost of machine = ₹ 40000.

(iii) Value of machine at beginning of third year = Original value - Depreciation in first and second years

= ₹ 40000 - (₹ 4000 + ₹ 3600)

= ₹ 40000 - ₹ 7600

= ₹ 32400.

For third year :

P = ₹ 32400

T = 1 year

Depreciation % = 10%

Depreciation = $\dfrac{P \times R \times T}{100} = \dfrac{32400 \times 10 \times 1}{100}$ = ₹3240.

Value at the end of third year = ₹ 32400 - ₹ 3240 = ₹ 29160.

Hence, value of machine at the end of third year = ₹ 29160.