Two equals sums were lent out at 7% and 5% S.I. respectively,. The interest earned on the two loans add up to Rs 960 for 4 years . The total sum lent out in

Options

A. Rs 3500
B. Rs 2500
C. Rs 2000
D. Rs 3000

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI), which is:

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

where:
- \( P \) is the principal amount (the sum lent out),
- \( R \) is the rate of interest,
- \( T \) is the time in years.

### Step 1: Define the variables
Let the principal amount lent out for each sum be \( x \).

### Step 2: Calculate the interest for both sums
1. For the first sum lent at 7% for 4 years:
\[ \text{SI}_1 = \frac{x \times 7 \times 4}{100} = \frac{28x}{100} \]

2. For the second sum lent at 5% for 4 years:
\[ \text{SI}_2 = \frac{x \times 5 \times 4}{100} = \frac{20x}{100} \]

### Step 3: Set up the equation for total interest
According to the problem, the total interest earned from both loans is Rs 960. Therefore, we can write:
\[ \text{SI}_1 + \text{SI}_2 = 960 \]
Substituting the values we calculated:
\[ \frac{28x}{100} + \frac{20x}{100} = 960 \]

### Step 4: Combine the terms
Combine the fractions:
\[ \frac{28x + 20x}{100} = 960 \]
\[ \frac{48x}{100} = 960 \]

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 100:
\[ 48x = 96000 \]
Now, divide both sides by 48:
\[ x = \frac{96000}{48} = 2000 \]

### Step 6: Calculate the total sum lent out
Since there are two equal sums, the total sum lent out is:
\[ \text{Total Sum} = 2x = 2 \times 2000 = 4000 \]

### Final Answer
The total sum lent out is Rs 4000.

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