Question

Simple interest on an amount at $4\%$ per annum for $13$ months is more than the simple interest on the same sum for $8$ months at $6\%$ per annum by $₹40$ what is the principal amount.

Answer 1

To find the principal amount.

Given

Interest for $13$ months at $4\%$

Interest per year $=4\%$

interest per month $=\frac{4}{12}=\frac{1}{3}\%$

Interest for $13$ months $=\frac{1}{3}\times 13=\frac{13}{3}\%$

Interest for $8$ months at $6\%$

interest per year $=6\%$

interest per month $=\frac{6}{12}=\frac{1}{2}$

interest for $8$ months $=\frac{1}{2}\times 8=4\%$

Let the principal amount be $x$

$$\begin{gathered} \frac{13}{3}\%ofx–4\%ofx=40 \\ \frac{1}{3}\%ofx=40 \\ 1\%ofx=120 \\ 100\%ofx=120\times 100=12000 \end{gathered}$$

Hence, the principal amount is $₹12000$.