`₹5000` yields `₹100` more aas interest than `₹4000`, if both the sums are invested at the same rate of interest per anuum for `2` years. Find the rate of interest.

Answer

To find the rate of interest, we will use the formula for Simple Interest (SI):

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest per annum,
- \( T \) is the time in years.

### Step 1: Calculate Simple Interest for ₹5000
For the first principal amount of ₹5000:

\[ \text{SI}_1 = \frac{5000 \times R \times 2}{100} \]

### Step 2: Calculate Simple Interest for ₹4000
For the second principal amount of ₹4000:

\[ \text{SI}_2 = \frac{4000 \times R \times 2}{100} \]

### Step 3: Set up the equation based on the problem statement
According to the problem, ₹5000 yields ₹100 more interest than ₹4000:

\[ \text{SI}_1 = \text{SI}_2 + 100 \]

Substituting the values of SI1 and SI2 from steps 1 and 2:

\[ \frac{5000 \times R \times 2}{100} = \frac{4000 \times R \times 2}{100} + 100 \]

### Step 4: Simplify the equation
First, we can cancel the common terms (the factor of 2/100) from both sides:

\[ 5000R = 4000R + 100 \]

### Step 5: Rearranging the equation
Now, we move \( 4000R \) to the left side:

\[ 5000R - 4000R = 100 \]

This simplifies to:

\[ 1000R = 100 \]

### Step 6: Solve for R
Now, divide both sides by 1000:

\[ R = \frac{100}{1000} = 0.1 \]

### Step 7: Convert to percentage
To convert \( R \) into a percentage, we multiply by 100:

\[ R = 0.1 \times 100 = 10\% \]

### Final Answer
The rate of interest is **10%**.

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