A sum becomes 5 times of itself in 3 years at compound interest (interest is compounded annually). In how many years will the sum becomes 125 times of itself?

Let principal be Rs.P
Then, Amount after 3 years will be Rs.5P
Let the rate of interest  be R%
$$P(1+\dfrac{R}{100})^3 = 5P$$

$$(1+\dfrac{R}{100})^3 = 5$$

=> $$(1+\dfrac{R}{100}) = 5^\frac{1}{3}$$ -- (1)

Let the amount after T years be Rs.125P
$$P(1+\dfrac{R}{100})^T = 125P$$

Substituting (1) in above equation
$$(5^\frac{1}{3})^T = 125$$

=> $$5^\frac{T}{3} = 5^3$$

=> $$\dfrac{T}{3} = 3$$

=> T = 9
Hence, In 9 years, the given principal becomes 125 times of itself.