Question

A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is \(25:8\). The rate of interest per annum is

• A. \(%\)\(10\%\)
• B. \(%\)\(11\%\)
• C. \(%\)\(12\%\)
• D. \(%\)\(12\%\)

Answer 1

The Correct Option is D

The correct option is (D): \(%\)Let principal sum be Rs.\(P\) and rate of interest=\(r\%\)
Difference between S.I. and C.I.
For 2 years =\(\frac{ Pr^{2} }{ 100^{2} } \) 
For 3 years = \(\frac{ Pr^{2} }{ 100^{2} } (3+\frac{r}{100})\)
Ratio = \(\frac{ Pr^{2} }{ 100^{2} } (3+\frac{r}{100})\)\(:\)\(\frac{ Pr^{2} }{ 100^{2} } \)= \(25:8\)
\(\frac{3+\frac{r}{100}}{1}\)=\(\frac{25}{8}\)
\(\frac{r}{100}=\frac{25}{8}-3\)
r=\(\frac{100}{8}=12\frac{1}{2}\%\)