Question

On what sum of money will the difference between simple interest and compound interest for 2 years at 10 % per annum be ₹ 27

• A. ₹ 2700
• B. ₹ 2500
• C. ₹ 2000
• D. ₹ 1800

Answer 1

The correct option is A

₹ 2700

Given R = 10 % Difference in S.I and C.I = ₹ 27 ; Period (n) = 2 years

Let the sum of money be P

C.I = P × ${[1+\frac{R}{100}]}^n$ - P

= P × ${[1+\frac{10}{100}]}^2$ - P

= P x ${[1+\frac{1}{10}]}^2$ - P

= P x ${\left[\frac{11}{10}\right]}^2$ - P

= P x $\left[\frac{121}{100}\right]$ - P

= $\frac{21P}{100}$

S.I = $\frac{P\times 10\times 2}{100}$

$\frac{P\times 10\times 2}{100}$
= $\frac{P}{5}$

Given the difference is 27
Hence $\frac{21P}{100}$ - $\frac{P}{5}$ = ₹ 27
$\frac{P}{100}$ = ₹ 27
P =₹ 2700