Question

Simple interest on a certain sum for $2\frac{5}{2}years$ at $10\%p.a.$is $Rs975$more than the simple interest on the same sum for $3\frac{1}{2}years$ at $8\%p.a.$find the sum and what will be the amount in $4years$ at $7\%p.a.$simple interest.

Answer 1

Let the Principal be $RsP$.

$$\begin{gathered} R_1=10\%p.a. \\ {T}_1=2\frac{5}{2}Y=\frac{9}{2}Y \\ {R}_2=8\%p.a. \\ {T}_2=3\frac{1}{2}Y=\frac{7}{2}Y \\ ChangeinSI=Rs975 \\ \frac{P\times R_1\times T_1}{100}-\frac{P\times R_2\times T_2}{100}=975 \\ \frac{P}{100}\left[R_1\times T_1-R_2\times T_2\right]=975 \\ \frac{P}{100}\left[10\times \frac{9}{2}-8\times \frac{7}{2}\right]=975 \\ \frac{P}{100}\left[45-28\right]=975 \\ \frac{17P}{100}=975 \\ 17P=975\times 100 \\ P=\frac{97500}{17}=Rs5735.29 \end{gathered}$$

$$\begin{gathered} Now, \\ R=7\%p.a. \\ T=4years \\ SI=\frac{P\times R\times T}{100}=\frac{5735.29\times 7\times 4}{100}=Rs3326.46 \\ A=P+I=5735.29+3326.46=Rs9061.75 \end{gathered}$$