Interest earned on `₹9000` is `₹400` more than the interest earned on `₹7000`. If both the sums are invested at the same rate of interest for `4` years, find the rate of interest.

Answer

To solve the problem step by step, we will use the formula for simple interest and the information given in the question.

### Step 1: Understand the Simple Interest Formula
The formula for simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 2: Calculate Simple Interest for Both Amounts
Let’s denote:
- \( SI_1 \) as the simple interest on ₹9000
- \( SI_2 \) as the simple interest on ₹7000

For \( SI_1 \):
\[ SI_1 = \frac{9000 \times R \times 4}{100} = \frac{36000R}{100} = 360R \]

For \( SI_2 \):
\[ SI_2 = \frac{7000 \times R \times 4}{100} = \frac{28000R}{100} = 280R \]

### Step 3: Set Up the Equation Based on Given Information
According to the problem, the interest earned on ₹9000 is ₹400 more than the interest earned on ₹7000. Therefore, we can write the equation as:
\[ SI_1 = SI_2 + 400 \]

Substituting the values we found:
\[ 360R = 280R + 400 \]

### Step 4: Solve for R
Now, we will solve the equation for \( R \):
\[ 360R - 280R = 400 \]
\[ 80R = 400 \]
\[ R = \frac{400}{80} = 5 \]

### Step 5: Conclusion
The rate of interest \( R \) is \( 5\% \).