Hari invested an amount at a certain rate of interest on simple interest and he got 60% more amount after eight years. If he invests Rs. 9600 at the same rate of interest on simple interest, then find the total interest he would get after four years?
We are given that Hari got 60% more amount after 8 years under simple interest. This means:
\[
\text{Total Amount} = \text{Principal} + \text{Simple Interest}
\]
\[
\text{Simple Interest} = 60\% \text{ of Principal} = \frac{60}{100} P = 0.6 P
\]
Using the formula for Simple Interest:
\[
SI = \frac{P \times R \times T}{100}
\]
where:
\( P \) = Principal
\( R \) = Rate of Interest per annum
\( T \) = Time in years
For 8 years:
\[
0.6 P = \frac{P \times R \times 8}{100}
\]
Cancel \( P \) (since \( P \neq 0 \)):
\[
0.6 = \frac{8R}{100}
\]
\[
R = \frac{0.6 \times 100}{8} = \frac{60}{8} = 7.5\%
\]
Step 2: Find Interest for Rs. 9600 Over 4 Years
Using the Simple Interest formula again for Rs. 9600 over 4 years:
\[
SI = \frac{9600 \times 7.5 \times 4}{100}
\]
\[
SI = \frac{9600 \times 30}{100}
\]
\[
SI = \frac{288000}{100} = 2880
\]
Final Answer
The total interest Hari would get after 4 years is:
\(
Rs. 2880
\)
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