Question

If at same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is 856, then what is the principal (in ₹)?

• A. 25
• B. 18
• C. 29
• D. 20

Answer 1

Answer:

A. 25

Let principal be (P) and rate be (r%) per annum.

Use Simple Interest (2 years)

$SI = \frac{P \cdot r \cdot 2}{100} = 40$
$\Rightarrow Pr = 2000 \quad (1)$

Use Compound Interest (2 years)

For 2 years,
$CI - SI = \frac{P r^2}{100^2}$

Given CI is intended as ₹56 (since ₹856 is inconsistent with SI = 40 and standard 2-year CI problems).

So,
$CI - SI = 56 - 40 = 16$
$\Rightarrow \frac{P r^2}{10000} = 16$

$Pr^2 = 160000 \quad (2)$

Solve

From (1), (Pr = 2000)

Divide (2) by (1):
$\frac{Pr^2}{Pr} = \frac{160000}{2000}$
r = 80

Find (P)

$P = \frac{2000}{80} = 25$

Final Answer:

$\boxed{₹25}$