Question

If at same rate of interest , in 2 years the simple interest is INR 42 and compound interest is INR 51, Then what is the principal (in INR) ?

• A. 44
• B. 49
• C. 42
• D. 53

Answer 1

Answer:

B. 49

Given:
Simple Interest (SI) for 2 years = 42
Compound Interest (CI) for 2 years = 51
Rate of interest is the same.

difference between CI and SI

For 2 years,
$\text{CI} - \text{SI} = \text{Interest on interest}$
$51 - 42 = 9$

For 2 years,

$\text{CI} - \text{SI} = P\left(\frac{r}{100}\right)^2$
$P\left(\frac{r}{100}\right)^2 = 9 \quad \text{(1)}$

Also, Simple Interest formula:

$\text{SI} = \frac{P \times r \times t}{100}$
$42 = \frac{P \times r \times 2}{100}$
$P \times r = 2100 \quad \text{(2)}$

From (2):
$r = \frac{2100}{P}$

Substitute in (1):
$P \left(\frac{2100}{100P}\right)^2 = 9$
$P \times \frac{441}{P^2} = 9$
$\frac{441}{P} = 9$
$P = 49$