Question

The value of a flat worth Rs. 500000 is depreciating at the rate of $10\%$ per annum. In how many years will its value be reduced to Rs. 364500?

• A. 4
• B. 3
• C. 5
• D. 2

Answer 1

The correct option is B

3

We have,
Present value = Rs. 500000, Depreciated value = Rs. 364500
Rate of depreciation $=10\%$ per annum.
Let the depreciation period be $n$ years. Then,
$364500=500000{(1-\frac{10}{100})}^n$
$\Rightarrow \frac{3645}{5000}={\left(\frac{9}{10}\right)}^n$
$\Rightarrow \frac{729}{1000}={\left(\frac{9}{10}\right)}^n\Rightarrow {\left(\frac{9}{10}\right)}^3={\left(\frac{9}{10}\right)}^n\Rightarrow n=3$
Hence, in 3 years the value of the flat be reduced to Rs. 364500.