Question

A certain sum of money lent out at 18.3% per annum produces the same simple interest in 6 years as rupees 3200 lent out at 42 upon 5% per annum for 7 years find the sum

Answer 1

Dear Student,


$$\begin{gathered} Interestearnedonacertainsumofmoneyat18.3\%for6years \\ SI=\frac{PRT}{100} \\ =\frac{P\times 18.3\times 6}{100} \\ Interestearnedon3200at\frac{42}{5}\%for7years \\ SI=\frac{3200\times \frac{42}{5}\times 7}{100} \\ Sinceboththeinterestaresame \\ \frac{P\times 18.3\times 6}{100}=\frac{3200\times \frac{42}{5}\times 7}{100} \\ \Rightarrow P\times 18.3\times 6=3200\times \frac{42}{5}\times 7 \\ \Rightarrow P\times 18.3\times 30=3200\times 42\times 7 \\ \Rightarrow P=\frac{3200\times 42\times 7}{18.3\times 30} \\ =\frac{320\times 14\times 7}{18.3} \\ =\frac{31360}{18.3} \\ =1713.66 \\ Hencetheamountinveestedis1713.66 \end{gathered}$$

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