At a simple interest a sum amount to ₹1012 in `2(1)/(2)`yr and becomes ₹1067.20 in 4yr.What is the rate of intrerest ?

Options

A. 0.25
B. 0.03
C. 0.04
D. 0.05

Answer

To find the rate of interest based on the given information, we can follow these steps:

### Step 1: Identify the given values
- Amount after 2.5 years (A1) = ₹1012
- Amount after 4 years (A2) = ₹1067.20
- Time for A1 (T1) = 2.5 years
- Time for A2 (T2) = 4 years

### Step 2: Convert the time into a fraction
- T1 = 2.5 years = \( \frac{5}{2} \) years
- T2 = 4 years

### Step 3: Use the formula for the rate of interest
The formula to find the rate of interest (R) is:
\[ R = \frac{A1 - A2}{A2 \times (T1 - T2)} \times 100 \]

### Step 4: Calculate the difference in amounts
- A1 - A2 = ₹1012 - ₹1067.20 = -₹55.20

### Step 5: Calculate the time difference
- T1 - T2 = 2.5 - 4 = -1.5 years

### Step 6: Substitute the values into the formula
Now substituting the values into the formula:
\[ R = \frac{-55.20}{1067.20 \times (-1.5)} \times 100 \]

### Step 7: Calculate the denominator
- Denominator = 1067.20 × -1.5 = -1600.8

### Step 8: Substitute the denominator back into the formula
\[ R = \frac{-55.20}{-1600.8} \times 100 \]

### Step 9: Calculate the rate of interest
- R = \( \frac{55.20}{1600.8} \times 100 \)
- R ≈ 3.44%

### Final Answer
The rate of interest is approximately **3.44%**.

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