A building worth ₹ 1,33,100 is constructed on land worth ₹ 72,900. After how many years will the value of both be the same if land appreciates at 10\% p.a. and building depreciates at 10\% p.a.?
(a)$1 \frac{1}{2}$
(b)2
(c)$2 \frac{1}{2}$
(d)3
Answer
Answer (as printed): D
Explanation
Let the required time be $n$ years. Then, $$\begin{aligned} & 72900 \times\left(1+\frac{10}{100}\right)^{n}=133100 \times\left(1-\frac{10}{100}\right)^{n} \Leftrightarrow\left(\frac{11}{10}\right)^{n} \times\left(\frac{10}{9}\right)^{n} \\ & =\frac{133100}{72900} \Leftrightarrow\left(\frac{11}{9}\right)^{n}=\frac{1331}{729}=\left(\frac{11}{9}\right)^{3} \Leftrightarrow n=3 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.