What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

Explanation:-

$$\eqalign{ & {1^{st}}\,{\text{case}}: \cr & {I_1} = \frac{{700 \times 3 \times 8}}{{100}} = Rs.\,168 \cr & {2^{nd}}\,{\text{case}}: \cr & {I_2} = \frac{{700 \times 2 \times 7.5}}{{100}} = Rs.\,105 \cr & {\text{Then}}\,{\text{total}}\,{\text{interest}}\,{\text{for}}\,{\text{five}}\,{\text{years}} \cr & = \left( {{I_1} + {I_2}} \right) = Rs.\,273 \cr & \cr & {\text{Alternatively}}, \cr & {\text{As}}\,{\text{interest}}\,{\text{is}}\,{\text{calculated}}\,{\text{as}}\,{\text{simple}}\,{\text{interest}}\, \cr & {\text{so}}\,{\text{we}}\,{\text{can}}\,{\text{add}}\,{\text{up}}\,{\text{rates}}\,{\text{for}}\,{\text{all}}\,{\text{given}}\,{\text{5}}\,{\text{years}}\,{\text{and}}\, \cr & {\text{calculate}}\,{\text{it}}\,{\text{easily}}\,i.e. \cr & {\text{For}}\,{\text{the}}\,{\text{five}}\,{\text{years}}\,{\text{rate}} \cr & = \left( {8 \times 3 + 7.5 \times 2} \right) = 39\% \cr & {\text{Now}}, \cr & 700 - - 39\% \uparrow - - > 973 \cr & {\text{Interest}} = Rs.\,273 \cr & {\text{The}}\,{\text{thought}}\,{\text{can}}\,{\text{go}}\,{\text{this}}\,{\text{way,}}\,{\text{we}}\,{\text{internally}}\,{\text{calculated}}\, \cr & 10\% \,{\text{of}}\,700 = \left( {\frac{{700}}{{10}}} \right) = 70. \cr & {\text{Then}},\,39\% \,{\text{of}}\,700 = \left( {40\% - 1\% } \right)\,{\text{of}}\, \cr & 700 = \left( {280 - 7} \right) = 273 \cr}$$