Question

The value of a machine depreciates at the rate of $10\%$ every year. it was purchased $3$ years ago . If its present value is Rs. $8748$, its purchase price was

• A. Rs. $10000$
• B. Rs. $11372$
• C. Rs. $12000$
• D. Rs. $12500$

Answer 1

The correct option is C Rs. $12000$

We know that

Final price $=$ initial price${(1+\frac{rate}{100})}^{time}$

Here the final price $=$ Rs. $8784$, time $=3$ yrs, rate $=-10\%$p.a.

The rate is negative since the price is depriciating.

Let the initial price $=$ Rs. $x$.

$\therefore x\times {(1-\frac{10}{100})}^3=8748$

$\Rightarrow x\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}=8748$

$\Rightarrow x=8748\times \frac{10}{9}\times \frac{10}{9}\times \frac{10}{9}=$ Rs. $12000$

So, the price of the machine $3$ years back $=$ Rs. $12000$.

Ans- Option C.