What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

1Rs. 5
2Rs. 10
3Rs. 20
4Rs. 40

Answer:- 1

Explanation:-

Solution:

\begin{aligned} I_{1} = \frac{P T_{1} R_{1}}{100} \\ I_{1} = \frac{(500 \times 3 \times 5)}{100} = R s . 75 \\ I_{1} = \frac{P T_{2} R_{2}}{100} \\ I_{2} = \frac{(500 \times 4 \times 4)}{100} = R s . 60 \\ Difference = R s . 5 \\ Alternatively, \\ The interest is calculated simply and then it will have \\ a rise of 15 % in 1^{s t} case and 16 % in 2^{n d} case . \\ Difference = 1 % on 500 = R s . 5 \\ Otherwise, \\ 500 - - 15 % ↑ - - > 575 (1^{s t} case) \\ 500 - - 16 % ↑ - - > 580 (2^{n d} case) \\ We can see clear difference of R s . 5 \end{aligned}

$\eqalign{ & {I_1} = \frac{{P{T_1}{R_1}}}{{100}} \cr & {I_1} = \frac{{\left( {500 \times 3 \times 5} \right)}}{{100}} = Rs.\,75 \cr & {I_1} = \frac{{P{T_2}{R_2}}}{{100}} \cr & {I_2} = \frac{{\left( {500 \times 4 \times 4} \right)}}{{100}} = Rs.\,60 \cr & {\text{Difference}} = Rs.\,5 \cr & \cr & {\text{Alternatively}}, \cr & {\text{The}}\,{\text{interest}}\,{\text{is}}\,{\text{calculated}}\,{\text{simply}}\,{\text{and}}\,{\text{then}}\,{\text{it}}\,{\text{will}}\,{\text{have}}\, \cr & {\text{a}}\,{\text{rise}}\,{\text{of}}\,15\% \,{\text{in}}\,{1^{st}}\,{\text{case}}\,{\text{and}}\,16\% \,{\text{in}}\,{2^{nd}}\,{\text{case}}. \cr & {\text{Difference}} = 1\% \,{\text{on}}\,500 = Rs.\,5 \cr & \cr & {\text{Otherwise}},\, \cr & 500 - - 15\% \uparrow - - > 575\,({1^{st}}\,{\text{case}}) \cr & 500 - - 16\% \uparrow - - > 580\,({2^{nd}}\,{\text{case}}) \cr & {\text{We}}\,{\text{can}}\,{\text{see}}\,{\text{clear}}\,{\text{difference}}\,{\text{of}}\,Rs.\,5 \cr}$