A person lent a certain sum of money at `4%` simple interest and in 5 years, the interest amounted to Rs. 520 less than the sum lent. The sum lent was

Options

A. Rs. 600
B. Rs. 650
C. Rs. 700
D. Rs. 750

Answer

To solve the problem step by step, we will use the information given in the question about simple interest.

### Step 1: Understand the variables
Let the principal amount (the sum lent) be represented by \( P \).

### Step 2: Identify the interest
According to the problem, the interest earned in 5 years is Rs. 520 less than the principal amount. Therefore, we can express the interest as:
\[ \text{Interest} = P - 520 \]

### Step 3: Use the simple interest formula
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal amount
- \( R \) is the rate of interest (4% in this case)
- \( T \) is the time in years (5 years in this case)

Substituting the values into the formula:
\[ SI = \frac{P \times 4 \times 5}{100} \]
This simplifies to:
\[ SI = \frac{20P}{100} = \frac{P}{5} \]

### Step 4: Set up the equation
Now, we equate the two expressions for interest:
\[ P - 520 = \frac{P}{5} \]

### Step 5: Clear the fraction
To eliminate the fraction, multiply both sides of the equation by 5:
\[ 5(P - 520) = P \]

### Step 6: Distribute and simplify
Distributing the 5 on the left side gives:
\[ 5P - 2600 = P \]

### Step 7: Rearrange the equation
Now, we can rearrange the equation to isolate \( P \):
\[ 5P - P = 2600 \]
This simplifies to:
\[ 4P = 2600 \]

### Step 8: Solve for \( P \)
Now, divide both sides by 4 to find \( P \):
\[ P = \frac{2600}{4} = 650 \]

### Conclusion
The sum lent was Rs. 650.

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