On a certain sum, the compound interest accrued in one year is ₹ 550. If the rate of interest is 10%, the sum is :

1. ₹ 5000

2. ₹ 6000

3. ₹ 4500

4. ₹ 5500

Given,

r = 10%

n = 1 year

C.I. = ₹ 550

Let sum of money lent out be ₹ x.

By formula,

C.I. = A - P

$\Rightarrow C.I. = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] \Rightarrow 550 = x(1 + \dfrac{10}{100})^1 - x \\[1em] \Rightarrow 550 = x + \dfrac{10x}{100} - x \\[1em] \Rightarrow 550 = \dfrac{x}{10} \\[1em] \Rightarrow x = 5500.$

Hence, Option 4 is the correct option.