Rohit invested a sum at a certain rate of interest on simple interest and he got `40%` more amount after four years. If he invests ₹7200 at the same rate of interest on SI, then find the total interest he would get after three years?

Options

A. ₹3840
B. ₹2160
C. ₹2520
D. ₹2340

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
Rohit invested a certain sum and received 40% more after 4 years. We need to find out how much interest he would earn if he invests ₹7200 at the same rate for 3 years.

### Step 2: Assume a principal amount
Let's assume Rohit initially invested ₹100. After 4 years, he received 40% more, which means he received:
\[ \text{Total Amount} = \text{Principal} + \text{Interest} = 100 + 40\% \text{ of } 100 = 100 + 40 = ₹140 \]

### Step 3: Calculate the interest earned
The interest earned over 4 years is:
\[ \text{Interest} = \text{Total Amount} - \text{Principal} = 140 - 100 = ₹40 \]

### Step 4: Use the simple interest formula
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal
- \(R\) = Rate of interest
- \(T\) = Time in years

From our assumption, we have:
- \(P = 100\)
- \(T = 4\) years
- \(SI = 40\)

We can now substitute these values into the formula to find the rate \(R\):
\[ 40 = \frac{100 \times R \times 4}{100} \]

### Step 5: Simplify to find the rate of interest
\[ 40 = 4R \]
\[ R = \frac{40}{4} = 10\% \]

### Step 6: Calculate the interest for ₹7200 over 3 years
Now, we need to find the interest if Rohit invests ₹7200 at the same rate of 10% for 3 years. Using the simple interest formula:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
- \(P = 7200\)
- \(R = 10\)
- \(T = 3\)

\[ SI = \frac{7200 \times 10 \times 3}{100} \]

### Step 7: Calculate the simple interest
\[ SI = \frac{72000}{100} = 720 \]

### Final Answer
The total interest Rohit would get after 3 years by investing ₹7200 at the same rate of interest is ₹720.

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