A man invested a sum at a certain rate of interest on simple interest and he got 60% more amount after eight year. If he invests Rs. 9600 at the same rate of interest on SI, then find the total interest he would get after four years?

Options

A. A)3840 Rs.
B. B)2880 Rs.
C. C)2520 Rs.
D. D)2160 Rs.

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Problem
A man invested a certain sum of money at a certain rate of simple interest (SI) and received 60% more after 8 years. We need to find out how much interest he would earn if he invests Rs. 9600 at the same rate for 4 years.

### Step 2: Determine the Interest Rate
Since the man received 60% more after 8 years, this 60% represents the total interest earned over that period.

Let the principal amount be \( P \). The total amount after 8 years is:
\[ A = P + \text{SI} \]
Given that SI is 60% of \( P \):
\[ \text{SI} = 0.6P \]
Thus, the total amount \( A \) after 8 years can be expressed as:
\[ A = P + 0.6P = 1.6P \]

### Step 3: Calculate the Interest for 4 Years
The interest earned in 8 years is 60%, which means the interest earned in 4 years would be half of that:
\[ \text{Interest for 4 years} = \frac{60\%}{2} = 30\% \]

### Step 4: Calculate the Simple Interest on Rs. 9600
Now, we will calculate the simple interest on Rs. 9600 for 4 years at the rate of 30%.

Using the formula for simple interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 9600 \)
- \( R = 30 \) (the rate of interest)
- \( T = 4 \) (the time period in years)

Substituting the values:
\[ \text{SI} = \frac{9600 \times 30 \times 4}{100} \]

### Step 5: Simplify the Calculation
Calculating the above expression:
\[ \text{SI} = \frac{9600 \times 120}{100} = \frac{1152000}{100} = 11520 \]

### Step 6: Final Calculation
Thus, the total interest earned after 4 years on Rs. 9600 at 30% simple interest is:
\[ \text{SI} = 2880 \]

### Conclusion
The total interest he would get after four years is Rs. 2880.

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