A person lent a certain sum of money at 12% per annum simple interst. In 5 years, the interest received was Rs. 250 less than the sum lent. Find the sum letn. (in Rs.)

Options

A. 500
B. 750
C. 625
D. 1000

Explanation

To find the sum lent, we can follow these steps:

### Step 1: Understand the given information
We know the following:
- Rate of interest (R) = 12% per annum
- Time (T) = 5 years
- The interest received is Rs. 250 less than the sum lent.

### Step 2: Let the principal amount be P
Let the sum lent (principal) be denoted as P.

### Step 3: Express the interest received
According to the problem, the interest received after 5 years is Rs. 250 less than the principal amount. Therefore, we can express the interest (I) as:
\[ I = P - 250 \]

### Step 4: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ I = \frac{P \times R \times T}{100} \]
Substituting the values we have:
\[ I = \frac{P \times 12 \times 5}{100} \]

### Step 5: Set up the equation
Now we can set the two expressions for interest equal to each other:
\[ P - 250 = \frac{P \times 12 \times 5}{100} \]

### Step 6: Simplify the right side
Calculating the right side:
\[ \frac{P \times 12 \times 5}{100} = \frac{60P}{100} = \frac{3P}{5} \]
So the equation becomes:
\[ P - 250 = \frac{3P}{5} \]

### Step 7: Clear the fraction
To eliminate the fraction, we can multiply the entire equation by 5:
\[ 5(P - 250) = 3P \]
This simplifies to:
\[ 5P - 1250 = 3P \]

### Step 8: Rearrange the equation
Now, rearranging the equation gives us:
\[ 5P - 3P = 1250 \]
\[ 2P = 1250 \]

### Step 9: Solve for P
Now, divide both sides by 2:
\[ P = \frac{1250}{2} = 625 \]

### Conclusion
The sum lent (P) is Rs. 625.

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