The simple interset on a sum for 9 months at 8 % per annum is Rs. 270. What is the value is (in Rs.) of the sum ?

Options

A. 5200
B. 5400
C. 4500
D. 3600

Answer

To find the value of the sum (P) based on the given simple interest (SI), we can use the formula for simple interest:

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

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the sum we need to find)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Identify the given values
From the question, we have:
- \( SI = 270 \) Rs
- \( R = 8\% \)
- \( T = 9 \) months

### Step 2: Convert time into years
Since the time is given in months, we need to convert it into years:
\[ T = \frac{9}{12} = \frac{3}{4} \text{ years} \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the simple interest formula:
\[ 270 = \frac{P \times 8 \times \frac{3}{4}}{100} \]

### Step 4: Simplify the equation
To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ 270 \times 100 = P \times 8 \times \frac{3}{4} \]
\[ 27000 = P \times 8 \times \frac{3}{4} \]

### Step 5: Calculate \( P \)
Now, simplify the right side:
\[ P \times 8 \times \frac{3}{4} = P \times 6 \]
So we have:
\[ 27000 = P \times 6 \]

Now, divide both sides by 6 to solve for \( P \):
\[ P = \frac{27000}{6} = 4500 \]

### Conclusion
The value of the sum (P) is Rs. 4500.

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