The simple interest on a sum of Rs. 6800 for 18 months is Rs. 2244. What is the rate (in percent) of interset per annum ?

Options

A. 24
B. 18
C. 20
D. 22

Answer

To find the rate of interest per annum based on the given information, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (initial sum of money)
- \( R \) = Rate of interest per annum (in percent)
- \( T \) = Time (in years)

### Step 1: Identify the given values
From the question, we have:
- Principal \( P = 6800 \) Rs
- Simple Interest \( SI = 2244 \) Rs
- Time \( T = 18 \) months = \( \frac{18}{12} = 1.5 \) years

### Step 2: Substitute the values into the formula
We need to find the rate \( R \). Rearranging the formula to solve for \( R \):

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

Substituting the known values:

\[ R = \frac{2244 \times 100}{6800 \times 1.5} \]

### Step 3: Calculate the denominator
First, calculate \( 6800 \times 1.5 \):

\[ 6800 \times 1.5 = 10200 \]

### Step 4: Substitute the denominator back into the equation
Now substitute back into the equation for \( R \):

\[ R = \frac{2244 \times 100}{10200} \]

### Step 5: Calculate the numerator
Calculate \( 2244 \times 100 \):

\[ 2244 \times 100 = 224400 \]

### Step 6: Final calculation for \( R \)
Now, divide \( 224400 \) by \( 10200 \):

\[ R = \frac{224400}{10200} = 22 \]

### Conclusion
The rate of interest per annum is \( 22\% \).

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