The cost of a car, purchased 2 years ago, depreciates at the rate of 20% per year. If its present value is ₹ 3,15,600; find :

(i) its value after 2 years.

(ii) its value, when it was purchased 2 years ago.

(i) The present value of the car = ₹ 3,15,600

Depreciation during the 1st year = 20 % of ₹ 3,15,600 = $\dfrac{20}{100} \times ₹ 3,15,600$ = ₹ 63,120

Value of the car at the beginning of 2nd year = ₹ 3,15,600 - ₹ 63,120 = ₹ 2,52,480

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

Value of the car after the 2nd year = ₹ 2,52,480 - ₹ 50,496 = ₹ 2,01,984

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

(ii) 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 car 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 final value of the car = ₹ 64, original cost = ₹ 100

⇒ The total value of the car = ₹ 3,15,600

Original cost = $\dfrac{100}{64} \times 3,15,600$ = ₹ 4,93,125

Hence, the value of the car when purchased = ₹ 4,93,125.