Question

A building worth Rs. 133,100 is constructed on land worth Rs. 72,900. After how many years will the value of the both be the same if land appreciates at 10% p.a. and building depreciates at 10% p.a.?

• A. 2.5
• B. 2
• C. 1.5
• D. 3

Answer 1

The correct option is D 3

$72900{(1+\frac{10}{100})}^n=133100\times {(1-\frac{10}{100})}^n$

$\therefore {\left(\frac{11}{10}\right)}^n\times {\left(\frac{10}{9}\right)}^n=\frac{133100}{72900}=\frac{1331}{729}$

$\therefore {\left(\frac{11}{9}\right)}^n={\left(\frac{11}{9}\right)}^3$
$\Rightarrow n=3$