Question

A building worth Rs 133100 is constructed on land worth Rs 72900. After how many years will the value of both be same if the land appreciates at 10% p.a. and building depreciates at 10% p.a. ?

(a) \(1\frac{1}{2}\) years

(b) 2 years

(c) 2\(\frac{1}{2}\) years

(d) 3 years

Answer 1

(d) 3 years

Let the required time be t years. Then,

72900\(\big(1+\frac{10}{100}\big)^t\) = 133100\(\big(1-\frac{10}{100}\big)^t\)

\(\Rightarrow\) \(\big(\frac{11}{10}\big)^t\)x \(\big(\frac{10}{9}\big)^t\) = \(\big(\frac{11}{9}\big)^3\) \(\Rightarrow\)\(\big(\frac{11}{9}\big)^t\) = \(\big(\frac{11}{9}\big)^3\)

\(\Rightarrow\) t = 3 years.