The cost of a car, purchased 2 years ago, depreciates at the rate of 20% every year.If its present value is ₹ 2,52,480, find:

(i) its purchase price.

(ii) its value after 1 year.

(i) Let the original cost of the car = ₹ 100

Depreciation during the 1st year = 20 % of ₹ 100 = $\dfrac{20}{100} \times ₹ 100$ = ₹ 20

Value of the machine at the beginning of the 2nd year = ₹ 100 - ₹ 20 = ₹ 80

Depreciation during the 2nd year = 20 % of ₹ 80 = $\dfrac{20}{100} \times ₹ 80$ = ₹ 16

Value of the car after 2 years = ₹ 80 - ₹ 16 = ₹ 64

Now, the value of the car after 2 years = ₹ 64

⇒ The present value of the car = ₹ 2,52,480

Original cost = $\dfrac{100}{64} \times 2,52,480$ = ₹ 3,94,500

Hence, the value of the car when purchased = ₹ 3,94,500.

(ii) The present value of the car = ₹ 2,52,480

Depreciation during the 1st year = 20 % of ₹ 2,52,480 = $\dfrac{20}{100} \times ₹ 2,52,480$ = ₹ 50,496

Value of the machine after 1 year = ₹ 2,52,480 + ₹ 50,496 = ₹ 2,01,984

Hence, the value of the car after 1 year = ₹ 2,01,984.