Mark and Peter borrowed `₹2250` and `₹2500`, respectively, at the same rate of simple interest for `3` years. Peter pat `₹45` more as interest than what Mark paid. Find the rate of interest per annum.

Answer

To find the rate of interest per annum for Mark and Peter, we can follow these steps:

### Step 1: Define the Variables
Let:
- Principal amount for Mark (P1) = ₹2250
- Principal amount for Peter (P2) = ₹2500
- Rate of interest per annum = r%
- Time = 3 years

### Step 2: Write the Simple Interest Formula
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times r \times t}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- r = Rate of interest
- t = Time in years

### Step 3: Calculate Simple Interest for Mark and Peter
Using the formula, we can express the Simple Interest for both Mark and Peter:
- Simple Interest for Mark (SI1):
\[ SI1 = \frac{2250 \times r \times 3}{100} = \frac{6750r}{100} = 67.5r \]

- Simple Interest for Peter (SI2):
\[ SI2 = \frac{2500 \times r \times 3}{100} = \frac{7500r}{100} = 75r \]

### Step 4: Set Up the Equation Based on Given Information
According to the problem, Peter paid ₹45 more in interest than Mark:
\[ SI2 = SI1 + 45 \]
Substituting the values we calculated:
\[ 75r = 67.5r + 45 \]

### Step 5: Solve for r
Now, we will solve the equation for r:
\[ 75r - 67.5r = 45 \]
\[ 7.5r = 45 \]
\[ r = \frac{45}{7.5} = 6 \]

### Conclusion
The rate of interest per annum is **6%**.

---