Question

A manufacturer reckons that the value of a machine, which costs him ₹ 15625 , will depreciate each year by $20\%$. The estimated value at the end of $5yr$ is

• A. ₹ 5050
• B. ₹ 5120
• C. ₹ 5920
• D. ₹ 5150

Answer 1

Answer: (B)

At present cost of machine $=₹15625$
Now, after $1$ yr cost of machine $=15625-\frac{20}{100}\times 15625$
$=15625-3125$
$-₹12500$
After $2yr$ cost of machine $=12500-\frac{20}{100}\times 12500$
$=12500-2500=₹10000$
and so on.
Clearly, the cost of machine form a G.P. 15625, 12500 , $10000,\dots$ with first term $a=15625$, common ratio $(r)=\frac{4}{5}$
Now, the estimated value at the end of $5yr$ is given by
$T_6=a{r}^5=15625{\left(\frac{4}{5}\right)}^5$
$=15625\times \frac{4^5}{5^5}=5^6\times \frac{2^{10}}{5^5}$
$=5\times 1024=₹5120$
Note In depreciation, the cost value decreases every year.