Question

If at same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is ₹65, then what is the principal (in ₹)?

• A. 11
• B. 16
• C. 20
• D. 9

Answer 1

Answer:

B. 16

For 2 years:

Simple Interest (SI)

$\text{SI} = \frac{P \times r \times 2}{100} = 40$

$\Rightarrow Pr = 2000 \quad (1)$

Difference between CI and SI (for 2 years)

$\text{CI} - \text{SI} = 65 - 40 = 25$

For 2 years:
$\text{CI} - \text{SI} = \frac{P r^2}{10000}$

$\Rightarrow \frac{P r^2}{10000} = 25$

$\Rightarrow Pr^2 = 250000 \quad (2)$

Divide (2) by (1)

$\frac{Pr^2}{Pr} = \frac{250000}{2000}$

$\Rightarrow r = 125$

Find Principal

From (1):
$P \times 125 = 2000$
$\Rightarrow P = 16$

Final Answer:

Principal = ₹16