The difference between the compound and simple interest on a certain sum deposited for 2 years at 5% p.a. is ₹ 12. The sum will be :

1. ₹ 4,500

2. ₹ 4,600

3. ₹ 4,800

4. ₹ 5,000

By formula,

Given,

T = 2 years

r = 5%

Let sum of money be ₹ P.

By formula,

$S.I. = \dfrac{P \times R \times T}{100} \\[1em] = \dfrac{P \times 5 \times 2}{100} \\[1em] = \dfrac{P}{10}.$

By formula,

C.I. = A - P

$C.I. = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] = P\Big(1 + \dfrac{5}{100}\Big)^2 - P \\[1em] = P \times \Big(\dfrac{105}{100}\Big)^2 - P \\[1em] = P \times \Big(\dfrac{21}{20}\Big)^2 - P\\[1em] = P \times \dfrac{441}{400} - P \\[1em] = \dfrac{441P}{400} - P \\[1em] = \dfrac{441P - 400P}{400} \\[1em] = \dfrac{41P}{400}.$

Given,

Difference between S.I. and C.I. = ₹ 12

$\Rightarrow \dfrac{41P}{400} - \dfrac{P}{10} = 12 \\[1em] \Rightarrow \dfrac{41P - 40P}{400} = 12 \\[1em] \Rightarrow \dfrac{P}{400} = 12 \\[1em] \Rightarrow P = 400 \times 12 \\[1em] \Rightarrow P = ₹ 4,800.$

Hence, option 3 is correct option.