₹ 10 is the difference between C.I. and S.I. in 2 years and at 5% per annum. The principal amount is :

1. ₹ 4400

2. ₹ 4100

3. ₹ 4000

4. none of these

Let principal amount be ₹ x.

For S.I. :

P = ₹ x

R = 5%

T = 2 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 5 \times 2}{100} = \dfrac{x}{10}$.

For C.I. :

For first year :

P = ₹ x

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 5 \times 1}{100} = \dfrac{x}{20}$.

Amount = P + I = $x + \dfrac{x}{20} = \dfrac{21x}{20}$

For second year :

P = ₹ $\dfrac{21x}{20}$

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{\dfrac{21x}{20} \times 5 \times 1}{100} = \dfrac{21x}{400}$.

Amount = P + I = $\dfrac{21x}{20} + \dfrac{21x}{400} = \dfrac{420x + 21x}{400} = \dfrac{441x}{400}$.

C.I. = Final amount - Initial Principal

= $\dfrac{441x}{400} - x = \dfrac{441x - 400x}{400} = \dfrac{41x}{400}$.

Given,

Difference between S.I. and C.I. = ₹ 10

$\Rightarrow \dfrac{41x}{400} - x = 10 \\[1em] \Rightarrow \dfrac{41x - 40x}{400} = 10 \\[1em] \Rightarrow \dfrac{x}{400} = 10 \\[1em] \Rightarrow x = 4000.$

Hence, Option 3 is the correct option.