Question

If at same rate of interest, in 2 years, the simple interest is ₹44 and compound interest is ₹46, then what is the principal (in ₹)?

• A. 237
• B. 235
• C. 246
• D. 242

Answer 1

Answer:

D. 242

Let principal = (P), rate = (r%) per annum, time = 2 years.

Simple Interest (SI)

$SI = \frac{P \cdot r \cdot 2}{100} = 44$
$\Rightarrow \frac{Pr}{100} = 22 \quad \text{(1)}$

Difference between CI and SI

For 2 years:
$CI - SI = P\left(\frac{r}{100}\right)^2$

Given:
$46 - 44 = 2$
$\Rightarrow P\left(\frac{r}{100}\right)^2 = 2 \quad \text{(2)}$

Solve using (1) and (2)

From (1):
$\frac{r}{100} = \frac{22}{P}$

Substitute into (2):
$P \left(\frac{22}{P}\right)^2 = 2$
$P \cdot \frac{484}{P^2} = 2$
$\frac{484}{P} = 2$

P = 242
Principal = ₹242