A building worth Rs. 133100 is constructed on land worth Rs. 72900. 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. ?

Let the required time be n years
Then,
$$ \Leftrightarrow 72900 \times {\left( {1 + \frac{{10}}{{100}}} \right)^n} = $$      $$133100 \,\times $$  $${\left( {1 - \frac{{10}}{{100}}} \right)^n}$$
$$\eqalign{ & \Leftrightarrow {\left( {\frac{{11}}{{10}}} \right)^n} \times {\left( {\frac{{10}}{9}} \right)^n} = \frac{{133100}}{{72900}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = \frac{{1331}}{{729}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = {\left( {\frac{{11}}{9}} \right)^3} \cr & \Leftrightarrow n = 3 \cr} $$