Question

The simple interest on a certain sum for 5 years at 8% per annum is Rs 200 less than the simple interest on the sum for 3 years & 4 months at 18% per annum . find the sum.

Answer 1

Dear Student,

$$\begin{gathered} SI=\frac{prt}{100} \\ Letthesumofamountbex. \\ SIforxfor5yearsat8\%pa=SIforxfor3years4monthsat18\%pa-200 \\ \frac{x\times 5\times 8}{100}=\frac{x\times 3{\displaystyle \frac{1}{3}}\times 18}{100}-200 \\ \frac{40x}{100}=\frac{x\times {\displaystyle \frac{10}{3}}\times 18}{100}-200 \\ \frac{40x}{100}=\frac{180x}{300}-200 \\ \frac{40x}{100}=\frac{180x}{300}-\frac{60000}{300} \\ \frac{40x}{100}=\frac{180x-60000}{300} \\ 40x\times 3=180x-60000 \\ 180x-120x=60000 \\ 60x=60000 \\ x=1000. \\ SothesumofamountisRs.1000 \end{gathered}$$

Regards.