On a certain sum, the S.I. for 2 years is ₹ 2400. If the rate of interest is 10% p.a., then :

C.I. for 1st year is :

1. ₹ 1200

2. ₹ 1320

3. ₹ 1800

4. ₹ 2640

Let sum of money be ₹ x.

Given,

S.I. = ₹ 2400

Time = 2 years

Rate = 10%

By formula,

$\Rightarrow S.I. = \dfrac{P \times R \times T}{100} \\[1em] \Rightarrow 2400 = \dfrac{x \times 10 \times 2}{100} \\[1em] \Rightarrow x = \dfrac{2400 \times 100}{10 \times 2} \\[1em] \Rightarrow x = ₹ 12000.$

By formula,

C.I. = A - P

$C.I. = P\Big(1 + \dfrac{r}{100}\Big)^1 - P \\[1em] = 12000\Big(1 + \dfrac{10}{100}\Big)^1 - 12000 \\[1em] = 12000\Big(1 + \dfrac{1}{10}\Big)^1 - 12000 \\[1em] = 12000 \times \Big(\dfrac{11}{10}\Big)^1 - 12000 \\[1em] = 12000 \times \dfrac{11}{10} - 12000 \\[1em] = 13200 - 12000 \\[1em] = ₹ 1200.$

Hence, Option 1 is the correct option.