Question

A machine depreciates in value each year at the rate of $10\%$ of its previous value. However every second year there is some maintenance work, so that in that particular year depreciation is only $5\%$ of its previous value. If at the end of the fourth year the value of the machine stands at Rs. $146205$, then find the value of the machine at the start at the first year?

• A. Rs. $190000$
• B. Rs. $200000$
• C. Rs. $195000$
• D. Rs. $210000$

Answer 1

The correct option is B Rs. $200000$

Let the value of the machine, at the onset, be $x$ when $x$ is in Rs.

Here we shall apply the rule

Final value $=$ original value $\times {(1+rate)}^{time}$.

Here the rate will be negative since the value is depriciating.

For two yrs. the rate of depriciation is $10\%$.

$\therefore$ the value after $2$ yrs.

$=$ $x\times {(1-\frac{10}{100})}^2=x\times \frac{9}{10}\times \frac{9}{10}$.

As given, the rate of depriciation for next $2$ yrs $=5\%$

$\therefore$ The value after next $2$ yrs

$=$ $x\times \frac{9}{10}\times \frac{9}{10}\times {(1-\frac{5}{100})}^2$

$=x\times \frac{9}{10}\times \frac{9}{10}\times \frac{19}{20}\times \frac{19}{20}$

But the final value after $4$ yrs $=$ Rs. $146205$.

$\therefore x\times \frac{9}{10}\times \frac{9}{10}\times \frac{19}{20}\times \frac{19}{20}=146205$

$\Rightarrow x=\frac{146205\times 40000}{81\times 19\times 19}=5\times 40000$

$\Rightarrow x=$ Rs. $200000$.

So, $4$ yrs. back, the value of the machine was Rs. $200000$.