If ₹ 6000 earns C.I. = ₹ 1200 in 6 months; then the rate of interest per year is :

1. 40%

2. 15%

3. 20%

4. 24%

Let rate of interest be r%.

Given,

P = ₹ 6000

C.I. = ₹ 1200

By formula,

$\Rightarrow C.I. = P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2} - P \\[1em] \Rightarrow 1200 = 6000\Big(1 + \dfrac{r}{200}\Big)^{\dfrac{1}{2} \times 2} - 6000 \\[1em] \Rightarrow 1200 + 6000 = 6000\Big(1 + \dfrac{r}{200}\Big) \\[1em] \Rightarrow 7200 = 6000\Big(1 + \dfrac{r}{200}\Big) \\[1em] \Rightarrow \dfrac{7200}{6000} = \Big(1 + \dfrac{r}{200}\Big) \\[1em] \Rightarrow \dfrac{7200}{6000} - 1 = \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{7200 - 6000}{6000} = \dfrac{r}{200} \\[1em] \Rightarrow \dfrac{1200}{6000} = \dfrac{r}{200} \\[1em] \Rightarrow r = \dfrac{1200}{6000} \times 200 \\[1em] \Rightarrow r = 40\%$

Hence, Option 1 is the correct option.