A sum becomes Rs. 8800 in 4 years at simple interset at the yearly interst rate of 25 % per annum. What is the sum (in Rs.) ?

Options

A. 4400
B. 6600
C. 7040
D. 6400

Answer

To find the principal sum (P) that becomes Rs. 8800 in 4 years at a simple interest rate of 25% per annum, we can use the formula for calculating the amount (A) in simple interest:

\[ A = P + SI \]

Where:
- \( A \) = Total amount after time \( T \)
- \( P \) = Principal amount (the initial sum)
- \( SI \) = Simple Interest

The formula for Simple Interest (SI) is given by:

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

Where:
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Identify the known values
- Amount (A) = Rs. 8800
- Rate (R) = 25%
- Time (T) = 4 years

### Step 2: Calculate Simple Interest (SI)
Using the formula for SI:

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

We can express the amount as:

\[ A = P + SI \]

Substituting SI in the amount formula gives:

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

### Step 3: Substitute the known values into the equation
Now, substituting the known values into the equation:

\[ 8800 = P + \frac{P \times 25 \times 4}{100} \]

### Step 4: Simplify the equation
First, simplify the SI term:

\[ \frac{P \times 25 \times 4}{100} = \frac{100P}{100} = P \]

So, the equation becomes:

\[ 8800 = P + P \]

This simplifies to:

\[ 8800 = 2P \]

### Step 5: Solve for P
Now, divide both sides by 2 to find P:

\[ P = \frac{8800}{2} \]

\[ P = 4400 \]

### Final Answer:
The principal sum is Rs. 4400.

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