Question

A certain sum of money amounts to $Rs.756$ in $2$ years and to $Rs.873$ in $3\frac{1}{2}$ years at a certain rate of simple interest. What is the rate of interest per annum?

• A. $11\%p.a.$
• B. $12\%p.a.$
• C. $13\%p.a.$
• D. $14\%p.a.$

Answer 1

The correct option is C $13\%p.a.$

Amount in $2$ years $=$ Rs. $756$

Amount is $3\frac{1}{2}$ years $=$ Rs. $873$
$\therefore$ Interest for $1\frac{1}{2}$ years $=$ Rs. $873-$ Rs. $756=$ Rs. $117$
Interest for $2$ years $=\frac{117}{\frac{3}{2}}\times 2=\frac{117\times 2\times 2}{3}=$ Rs. $156$

Interest for $1$ year $=\frac{117\times 2}{3}=$ Rs. $78$
$\therefore$ Principal $=\text{Amount}-\text{Interest}$ ....(for $2$ years) $=$ Rs. $756-$ Rs. $156=$ Rs. $600$
$\therefore$ Rate of interest $=\frac{78\times 100}{600\times 1}=13\%$ p.a.