₹ 10000 amounts to ₹ 12500 in one year. The rate of interest per year is :

1. 15%

2. 12.5%

3. 20%

4. 25%

Let rate of interest be r%.

Given,

P = ₹ 10000

A = ₹ 12500

n = 1 year

By formula,

A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Substituting values we get :

$\Rightarrow 12500 = 10000 \times \Big(1 + \dfrac{r}{100}\Big)^1 \\[1em] \Rightarrow \dfrac{12500}{10000} = \Big(1 + \dfrac{r}{100}\Big) \\[1em] \Rightarrow \dfrac{5}{4} = 1 + \dfrac{r}{100}\\[1em] \Rightarrow \dfrac{5}{4} - 1 = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{5 - 4}{4} = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{1}{4} = \dfrac{r}{100} \\[1em] \Rightarrow r = \dfrac{100}{4} = 25\%.$

Hence, Option 4 is the correct option.