Question

A machine depreciates every year at the rate of 20% of its value at the beginning of the year. The machine was purchased for Rs. 2,50,000 when new and the scrap value realized when sold was Rs. 1,28,000. Find the number of years that the machine was used.

Answer 1

Let the required number of years be $n$
$\therefore$ Value of machine after n years = Its value when new ${(1-\frac{r}{100})}^n$ [Using the concept of compound interest]

Given that the initial value of the car is $Rs.250000$ and its value after $n$ years is $Rs.128000$

$\therefore Rs.128000=Rs.250000{(1-\frac{20}{100})}^n$

$\Rightarrow \frac{Rs.128000}{Rs.250000}={\left(\frac{80}{100}\right)}^n={\left(\frac{4}{5}\right)}^n$

On simplifying, we get :

${\left(\frac{4}{5}\right)}^3={\left(\frac{4}{5}\right)}^n\Rightarrow n=3years$