A man had Rs 16,000, part of which he lent at 4 % and the rest at 5 % per annum simple interset. If the total interset received was Rs 700 in one year, the money lent at 4 % per annum was

Options

A. Rs 12,000
B. Rs 8,000
C. Rs 10,000
D. Rs 6,000

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let \( x \) be the amount of money lent at 4% per annum. Therefore, the amount lent at 5% per annum will be \( 16000 - x \).

**Hint:** Identify the total amount and split it into two parts based on the interest rates.

### Step 2: Write the Simple Interest Formula
The formula for simple interest is given by:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest,
- \( T \) is the time in years.

### Step 3: Calculate the Interest for Each Part
1. Interest from the amount lent at 4%:
\[ \text{Interest at 4%} = \frac{x \times 4 \times 1}{100} = \frac{4x}{100} = 0.04x \]

2. Interest from the amount lent at 5%:
\[ \text{Interest at 5%} = \frac{(16000 - x) \times 5 \times 1}{100} = \frac{5(16000 - x)}{100} = 800 - 0.05x \]

### Step 4: Set Up the Equation
According to the problem, the total interest received from both parts is Rs 700. Therefore, we can set up the equation:
\[ 0.04x + (800 - 0.05x) = 700 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 0.04x - 0.05x + 800 = 700 \]
\[ -0.01x + 800 = 700 \]

### Step 6: Solve for \( x \)
Subtract 800 from both sides:
\[ -0.01x = 700 - 800 \]
\[ -0.01x = -100 \]
Now, divide both sides by -0.01:
\[ x = \frac{-100}{-0.01} = 10000 \]

### Step 7: Conclusion
The amount of money lent at 4% per annum is Rs 10,000.

**Final Answer:** Rs 10,000

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