The value of a fixed asset depreciates at the rate of 10\% of the value at the beginning of each year. If the value of the asset, two years ago, was ₹ 12000 more than the value of the asset one year ago, then find the present value of the asset, given that the asset was bought two years ago.
(a)₹ 14520
(b)₹ 17520
(c)₹ 96000
(d)₹ 97200
Answer
Answer (as printed): D
Explanation
Let the present value of the asset be ₹ $x$. Then, $$\begin{aligned} & \frac{x}{\left(1-\frac{10}{100}\right)^{2}}-\frac{x}{\left(1-\frac{10}{100}\right)}=12000 \Rightarrow \frac{x-x\left(1-\frac{10}{100}\right)}{\left(1-\frac{10}{100}\right)^{2}}=12000 \\ & \Rightarrow \frac{x}{10}=12000 \times \frac{9}{10} \times \frac{9}{10} \Rightarrow x=97200 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.