A sum of Rs. 1600/- gives a simple interest of Rs. 252/in 2 years and 3 months. The rate of interest per annum is:

Options

A. `5 1/2%`
B. `8%`
C. `7%`
D. `6%`

Answer

To find the rate of interest per annum, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 1600
- Simple Interest (SI) = Rs. 252
- Time (T) = 2 years and 3 months

### Step 2: Convert the time into years
To convert the time into years, we note that 3 months is equal to 3/12 years. Thus:
\[ T = 2 + \frac{3}{12} = 2 + \frac{1}{4} = \frac{9}{4} \text{ years} \]

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest per annum
- T = Time in years

### Step 4: Substitute the known values into the formula
Substituting the known values into the formula gives:
\[ 252 = \frac{1600 \times R \times \frac{9}{4}}{100} \]

### Step 5: Simplify the equation
First, we can rearrange the equation to isolate R:
\[ 252 = \frac{1600 \times R \times 9}{400} \]
Multiplying both sides by 400 to eliminate the fraction:
\[ 252 \times 400 = 1600 \times R \times 9 \]
Calculating the left side:
\[ 100800 = 14400R \]

### Step 6: Solve for R
Now, divide both sides by 14400 to find R:
\[ R = \frac{100800}{14400} \]
Calculating the division:
\[ R = 7 \]

### Step 7: Conclusion
The rate of interest per annum is:
\[ R = 7\% \]