Question

The simple interest on a certain sum of 5 years at 8%p.a is rs 200 less than the simple interest on the same sum for 3 years and 4 months at 18%p.a. Find the sum.

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ \mathrm{SI}=\frac{\mathrm{Prt}}{100}\mathrm{where}\mathrm{P}\mathrm{is}\mathrm{principal},\mathrm{t}\mathrm{is}\mathrm{time}\mathrm{and}\mathrm{r}\mathrm{is}\mathrm{rate} \\ \mathrm{so}\mathrm{here}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question} \\ \mathrm{in}\mathrm{first}\mathrm{case}\mathrm{r}=8\%,\mathrm{t}=5\mathrm{years} \\ \mathrm{SI}\mathrm{of}\mathrm{first}\mathrm{case}=\frac{\mathrm{P}\times 8\times 5}{100}=\frac{2\mathrm{P}}{5} \\ \mathrm{in}\mathrm{second}\mathrm{case},\mathrm{r}=18\%,\mathrm{t}=3\mathrm{years}4\mathrm{month}=3+\frac{4}{12}=\frac{10}{3}\mathrm{year} \\ \mathrm{SI}\mathrm{for}\mathrm{second}\mathrm{case}=\frac{\mathrm{P}\times 10\times 18}{3\times 100}=\frac{3\mathrm{P}}{5} \\ \mathrm{Difference}\mathrm{is}200\mathrm{so} \\ \frac{3\mathrm{P}}{5}-\frac{2\mathrm{P}}{5}=200 \\ \frac{\mathrm{P}}{5}=200 \\ \mathrm{So}\mathrm{principal}\mathrm{P}=\mathrm{Rs}.1000 \end{gathered}$$
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