A man borrowed Rs 16000 from two persons. He paid 6 % interest to one and 10 % per annum to the other. In one year he paid total interest Rs 1120. How much did he borrow at each rate ?

Options

A. Rs 10000 , Rs. 6000
B. Rs 120000 , Rs 4000
C. Rs 11000 , Rs 5000
D. Rs 12500 , Rs 3500

Answer

To solve the problem, we need to determine how much the man borrowed at each interest rate. Let's denote the amount borrowed at 6% as \( x \) and the amount borrowed at 10% as \( 16000 - x \).

### Step-by-Step Solution:

1. **Set Up the Variables:**
- Let \( x \) be the amount borrowed at 6%.
- Therefore, the amount borrowed at 10% is \( 16000 - x \).

2. **Write the Interest Formulas:**
- The interest paid on the amount borrowed at 6% for one year is:
\[ \text{Interest}_1 = \frac{6}{100} \times x = 0.06x \]
- The interest paid on the amount borrowed at 10% for one year is:
\[ \text{Interest}_2 = \frac{10}{100} \times (16000 - x) = 0.10(16000 - x) = 1600 - 0.10x \]

3. **Set Up the Total Interest Equation:**
- According to the problem, the total interest paid in one year is Rs 1120. Therefore, we can write the equation:
\[ 0.06x + (1600 - 0.10x) = 1120 \]

4. **Combine Like Terms:**
- Rearranging the equation gives:
\[ 0.06x - 0.10x + 1600 = 1120 \]
- This simplifies to:
\[ -0.04x + 1600 = 1120 \]

5. **Isolate \( x \):**
- Subtract 1600 from both sides:
\[ -0.04x = 1120 - 1600 \]
- This simplifies to:
\[ -0.04x = -480 \]
- Now, divide both sides by -0.04:
\[ x = \frac{-480}{-0.04} = 12000 \]

6. **Calculate the Amount Borrowed at 10%:**
- Now, substitute \( x \) back to find the amount borrowed at 10%:
\[ 16000 - x = 16000 - 12000 = 4000 \]

### Final Answer:
- Amount borrowed at 6%: Rs 12000
- Amount borrowed at 10%: Rs 4000