Question

A certain sum of money at simple interest amounts to Rs.1500 in 10 years and to Rs. 1725 in 13 years. Find the sum and rate of interest.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Now},\mathrm{A}=\mathrm{P}+\mathrm{I} \\ \mathrm{I}=\mathrm{A}-\mathrm{P}...\left(1\right) \\ \mathrm{and}\mathrm{also}, \\ \mathrm{I}=\frac{\mathrm{PRT}}{100}...\left(2\right) \\ \mathrm{Equating}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get} \\ \mathrm{A}-\mathrm{P}=\frac{\mathrm{PRT}}{100} \\ \mathrm{Case}1: \\ \mathrm{A}=\mathrm{Rs}1500,\mathrm{T}=10\mathrm{years} \\ \mathrm{So}, \\ 1500-\mathrm{P}=\frac{\mathrm{PR}\times 10}{100} \\ \Rightarrow 15000-10\mathrm{P}=\mathrm{PR} \\ \Rightarrow 15000=\mathrm{PR}+10\mathrm{P} \\ \Rightarrow 15000=\mathrm{P}\left(\mathrm{R}+10\right) \\ \Rightarrow \mathrm{P}=\frac{15000}{\mathrm{R}+10}...\left(\mathrm{a}\right) \\ \mathrm{Case}2: \\ \mathrm{A}=\mathrm{Rs}1725,\mathrm{T}=13\mathrm{years} \\ \mathrm{So}, \\ 1725-\mathrm{P}=\frac{\mathrm{PR}\times 13}{100} \\ \Rightarrow 172500-100\mathrm{P}=13\mathrm{PR} \\ \Rightarrow 172500=13\mathrm{PR}+100\mathrm{P} \\ \Rightarrow 172500=\mathrm{P}\left(13\mathrm{R}+100\right) \\ \Rightarrow 172500=\left(\frac{15000}{\mathrm{R}+10}\right)\left(13\mathrm{R}+100\right) \\ \Rightarrow \frac{23}{2}=\frac{13\mathrm{R}+100}{\mathrm{R}+10} \\ \Rightarrow 23\mathrm{R}+230=26\mathrm{R}+200 \\ \Rightarrow 3\mathrm{R}=30 \\ \Rightarrow \mathrm{R}=10 \\ \mathrm{and}\mathrm{P}=\frac{15000}{10+10}=750 \\ \mathrm{So},\mathrm{Sum},\mathrm{P}=\mathrm{Rs}750\mathrm{and}\mathrm{Rate}\mathrm{of}\mathrm{interest},\mathrm{I}=10\% \end{gathered}$$
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