The value of a gadget worth Rs. 10,000 is depreciating at the rate of 10% per year. In how many years will its value be reduced to Rs. 6,561?

Explanation

According to the question $$6561 = 10000 \left(1 - \frac{10}{100}\right)^n$$ $$6561 = 10000 \times \left(\frac{9}{10}\right)^n$$ $$\frac{6561}{10000} = \left(\frac{9}{10}\right)^n$$ $$\left(\frac{9}{10}\right)^4 = \left(\frac{9}{10}\right)^n$$ $\therefore n = 4$ years