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. ?
A. $$1\frac{1}{2}$$
B. 2
C. $$2\frac{1}{2}$$
D. 3
Answer: Option D
Solution(By Examveda Team)
Let the required time be n yearsThen,
$$ \Leftrightarrow 72900 \times {\left( {1 + \frac{{10}}{{100}}} \right)^n} = $$ $$133100 \,\times $$ $${\left( {1 - \frac{{10}}{{100}}} \right)^n}$$
$$\eqalign{ & \Leftrightarrow {\left( {\frac{{11}}{{10}}} \right)^n} \times {\left( {\frac{{10}}{9}} \right)^n} = \frac{{133100}}{{72900}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = \frac{{1331}}{{729}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = {\left( {\frac{{11}}{9}} \right)^3} \cr & \Leftrightarrow n = 3 \cr} $$
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
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