Question

If simple interest on a sum of money for $3$ years is Rs. $240$ and compound interest on the sum at same rate for $2$ years is Rs. $170$, then the rate $\%$ p.a. is

• A. $16\%$
• B. $8\%$
• C. $12\frac{1}{2}\%$
• D. $1\frac{1}{8}\%$

Answer 1

The correct option is C $12\frac{1}{2}\%$

simple interest for one year$=\frac{240}{3}=Rs.80$

simple Interest for two year$=80\times 2=Rs.160$

Compound interest for two years$=Rs.170$

Difference for $2$ year$=170-160=Rs.10$

Hence

$Rate\left(\%\right)=\frac{10}{80}\times 100$

$=12\frac{1}{2}\%$