The value of a flat worth ₹500,000 is depreciating at the rate of 10% per annum. In how many years will the value be reduced to ₹364,500?

The value of a flat worth ₹500,000 is depreciating at the rate of 10% per annum. Thus, at the end of the first year, the value of the flat will be = 500000(1 - 0.1) = 500000(0.9).

Thus, the value of flat at the end of the second year will be = 500000(0.9)(1 - 0.1) = 500000(0.9)(0.9)

Therefore, the value of the flat at the end of n years will be $$=500000\left(0.9\right)^n$$

This value is given as 364500.

$$500000\left(0.9\right)^n=364500$$

$$0.9^n=0.729$$

$$n=3$$ years