Question

The value of a car depreciates 20% every year. If after two years the price of a car is Rs.2,08,000, find the original price of the car.

Answer 1

Given:

Let the original price of the car $=Rs.x$

Percentage of depreciation per year $=20\%$

Time period $=2$ yrs

Price of a car after two years $=Rs.208000$

Amount of depreciation $A=P(1-\frac{r}{100}{)}^n,$

here $A$ is the amount after depreciation, $r$ is the rate of depreciation and $n$ is time.

$\Rightarrow 208000=x(1-\frac{20}{100}{)}^2$

$\Rightarrow 208000=x(\frac{100-20}{100}{)}^2$

$\Rightarrow 208000=x(\frac{80}{100}{)}^2$

$\Rightarrow 208000=x(\frac{4}{5}{)}^2$

$\Rightarrow 208000=x(\frac{16}{25})$

$\Rightarrow x=208000\times \frac{25}{16}$

$\Rightarrow x=Rs.325000$

$\therefore$ Original price of the car $=Rs.325000$