A and B borrowed Rs 3000 and Rs 3200 respectively at the same rate of interest for `2(1)/(2)` years. If B paid Rs 40 more interest than A. find the rate of interest.

Options

A. 5%
B. 7%
C. 8%
D. 6%

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 given information
- A borrowed Rs 3000.
- B borrowed Rs 3200.
- Both borrowed money for a time period of 2.5 years.
- B paid Rs 40 more interest than A.

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate the interest for A and B
Let the rate of interest be \( R \).

For A:
\[ \text{SI}_A = \frac{3000 \times R \times 2.5}{100} = \frac{7500R}{100} = 75R \]

For B:
\[ \text{SI}_B = \frac{3200 \times R \times 2.5}{100} = \frac{8000R}{100} = 80R \]

### Step 4: Set up the equation based on the information given
According to the problem, B paid Rs 40 more interest than A:
\[ \text{SI}_B = \text{SI}_A + 40 \]
Substituting the values we calculated:
\[ 80R = 75R + 40 \]

### Step 5: Solve for R
Now, simplify the equation:
\[ 80R - 75R = 40 \]
\[ 5R = 40 \]
\[ R = \frac{40}{5} = 8 \]

### Conclusion
The rate of interest \( R \) is **8%**.

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