If the compound interest on a certain sum for 2 years at 10% p.a. is ₹ 2,100, the simple interest on it at the same rate for 2 years will be:

1. ₹ 1,500

2. ₹ 1,800

3. ₹ 2,000

4. ₹ 2,050

Given,

C.I = ₹ 2,100

n = 2 years

R = 10%

By Formula,

C.I = Amount - Principal

C.I = $P \times \Big(1 + \dfrac{R}{100}\Big)^n$ - P

Substituting the values in formula

$\Rightarrow 2100 = P \times \Big(1 + \dfrac{10}{100}\Big)^2 - P\\[1em] \Rightarrow 2100 = P \times \Big(\dfrac{100 + 10}{100}\Big)^2 - P\\[1em] \Rightarrow 2100 = P \times \Big(\dfrac{110}{100}\Big)^2 - P\\[1em] \Rightarrow 2100 = P \times (1.10)^2 - P\\[1em] \Rightarrow 2100 = 1.21P - P \\[1em] \Rightarrow 2100 = 0.21P \\[1em] P = \dfrac{2100}{0.21} \\[1em] P = 10,000$

To calculate the simple interest on the same principal.

T = 2 years

I = $\dfrac{P \times R \times T}{100}$

Substituting the Values,

I = $\dfrac{10000 \times 10 \times 2}{100}$ = ₹ 2,000

Hence, Option 3 is correct option.