### 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?

A. Rs. 269.5 B. Rs. 283 C. Rs. 273 D. Rs. 280 Answer: Option C
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### Solution(By Apex Team)

$\begin{array}{l}\text{I}^{\text{st}}\ \text{case}\\ \text{I}_1=\frac{700\times3\times8}{100}=\text{ Rs. }168\\ 2^{\text{nd }}\text{ case : }\\ \text{I}_2=\frac{700\times2\times7.5}{100}=\text{ Rs. }105\\ \text{Then total interest for five years}\\ \text{= I}_1+\text{I}_2=\text{Rs.}\ 273\end{array}$
Alternate Method: 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% ↑ ⇒ 973 Interest = Rs. 273 The thought can go this way we internally calculated $10 \% \text { of } 700=\frac{700}{10}=70$ Then, $\begin{array}{l} 39 \% \text { of } 700 \\ =(40 \%-1 \%) \text { of } 700 \\ =(280-7) \\ =273 \end{array}$