Question

If at same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is ₹44, then what is the principal (in ₹)?

• A. 100
• B. 95
• C. 104
• D. 93

Answer 1

Answer:

A. 100

Given:

• Simple Interest (SI) for 2 years = ₹40

• Compound Interest (CI) for 2 years = ₹44

For 2 years,
$\text{CI} - \text{SI} = \frac{P \cdot r^2}{100^2}$
Find the difference

44 - 40 = 4
$\Rightarrow \frac{P \cdot r^2}{10000} = 4$

$P \cdot r^2 = 40000 \quad \text{(1)}$
Use SI formula

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

$P \cdot r = 2000 \quad \text{(2)}$
Divide (1) by (2)

$\frac{P r^2}{P r} = \frac{40000}{2000}$
r = 20%
Find (P)

$P \cdot r = 2000$
$P \cdot 20 = 2000$
P = 100
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