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

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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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