The cost of a car depreciates at the rate of 20% every year. If its present

Question

The cost of a car depreciates at the rate of

20 %

every year. If its present worth is ₹ 315600, find the purchase value of the car, if it was purchased two years back.

Options:

A . ₹ 4,93,125

B . ₹ 2,01,984

C . ₹ 4,10884

D . ₹ 2,22,884

Answer: Option A
:
A
Given that A =₹ 3,15,600 , r = 20 % ; n = 2 years.
Let P be the value of the car two years ago.

A = P (1 - \frac{20}{100})^{2}

315600 = P (1 - \frac{1}{5})^{2}

315600 = P (\frac{4 \times 4}{5 \times 5})

P = \frac{315600 \times 5 \times 5}{4 \times 4}

P = ₹ 4, 93, 125

∴ Purchase value of the car = ₹ 4, 93, 125

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