Question

Solve this:

15. At what rate per cent per annum will RS 1640 amount to RS 1968 in 5/2 years?

16. in what time will RS 1860 amount to RS 2348.25 is simple interest in calculated at 15/2% per annum?

17. A sum of money lent at simple interest amounts to RS 3224 in 2 years and RS 4160 in 5 years. Find the sum and the rate of interest.

Answer 1

Dear student,

Question 17)
$$\begin{gathered} Amountin5years=(Principal+S.I.for5years)=Rs.3224 \\ Amountin3years=(Principal+S.I.for3years)=Rs.4160 \\ Onsubtractiong \\ S.I.for2years=\left(4160-3224\right)=Rs936 \\ S.I.for3years=\frac{936}{2}\times 3=Rs1404 \\ \therefore Sum=Amountfor3years-S.I.for3years \\ =4160-1404 \\ =Rs2756 \\ P=Rs2756,S.I.=Rs1404,T=3years \\ R=\frac{SI\times 100}{P\times T} \\ =\frac{1404\times 100}{2756\times 3} \\ =\frac{468\times 100}{2756} \\ =\frac{117\times 100}{689} \\ =16.98\% \end{gathered}$$

Question 19)

$$\begin{gathered} LetthefirstpartbeRsx \\ SI=\frac{PRT}{100} \\ Then,SIforfirstpart=\frac{x\times 15\times \sout{2}}{100\times \sout{2}} \\ \Rightarrow SIforfirstpart=\frac{x\times 15}{100}=\frac{15x}{100} \\ Now,letthesecondpart=Rs\left(8000-x\right) \\ Now,SIforsecondpart=\frac{\left(8000-x\right)\times 8\times 3}{100} \\ \Rightarrow SIforsecondpart=\frac{\left(8000-x\right)\times 24}{100} \\ \Rightarrow SIforsecondpart=\frac{192000-24x}{100} \\ TotalSI=SIforfirstpart+SIforsecondpart \\ \Rightarrow 1416=\frac{15x}{100}+\frac{192000-24x}{100} \\ \Rightarrow 1416=\frac{15x+192000-24x}{100} \\ \Rightarrow 1416=\frac{192000-9x}{100} \\ \Rightarrow 141600=192000-9x \\ \Rightarrow 9x=192000-141600 \\ \Rightarrow 9x=50400 \\ \Rightarrow x=\frac{50400}{9} \\ \Rightarrow x=5600 \\ ThustheFirstpart=Rs5600 \\ andsecondpart=Rs\left(8000-5600\right)=Rs2400 \end{gathered}$$
Regards