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?

Solution(By Examveda Team)

$$\eqalign{ & {1^{{\text{st}}}}{\kern 1pt} {\text{case}}: \cr & {I_1} = \frac{{700 \times 3 \times 8}}{{100}} = {\text{Rs}}{\text{. }}168 \cr & {2^{{\text{nd}}}}{\kern 1pt} {\text{case}}: \cr & {I_2} = \frac{{700 \times 2 \times 7.5}}{{100}} = {\text{Rs}}{\text{. }}105 \cr} $$
Then total interest for five years
$$ = \left( {{I_1} + {I_2}} \right) = {\text{Rs}}{\text{. }}273$$

Alternatively,
As interest is calculated as simple interest
So, we can add up rates for all given 5 years and calculate it easily i.e.
For the five years rate
= (8 × 3 + 7.5 × 2)
= 39%
Now,
700 = 39% $$ \uparrow $$ ⇒ 973
Interest = Rs. 273
The thought can go this way we internally calculated
$$\eqalign{ & {\kern 1pt} 10\% \,{\text{of}}\,700 = {\frac{{700}}{{10}}} = 70 \cr & {\text{Then}}, \cr & 39\% \,{\text{of}}\,700 \cr & = \left( {40\% - 1\% } \right)\,{\text{of}}\,700 \cr & = \left( {280 - 7} \right) \cr & = 273 \cr} $$