The average monthly Income of A and B is Rs 14000, that of B and C Is Rs 15600 and A and C is Rs 14400. The monthly income of C is:

Options

A. Rs 16000
B. Rs 15000
C. Rs 14000
D. Rs 15500

Answer

To find the monthly income of C, we can use the information given about the averages of A, B, and C. Let's break it down step by step.

### Step 1: Set up the equations based on the averages
1. The average monthly income of A and B is Rs 14,000.
\[ \frac{A + B}{2} = 14000 \implies A + B = 28000 \quad \text{(Equation 1)} \]

2. The average monthly income of B and C is Rs 15,600.
\[ \frac{B + C}{2} = 15600 \implies B + C = 31200 \quad \text{(Equation 2)} \]

3. The average monthly income of A and C is Rs 14,400.
\[ \frac{A + C}{2} = 14400 \implies A + C = 28800 \quad \text{(Equation 3)} \]

### Step 2: Add all three equations
Now, we can add all three equations together:
\[ (A + B) + (B + C) + (A + C) = 28000 + 31200 + 28800 \]
This simplifies to:
\[ 2A + 2B + 2C = 88000 \]

### Step 3: Divide the sum by 2
To find the sum of A, B, and C, divide both sides by 2:
\[ A + B + C = 44000 \quad \text{(Equation 4)} \]

### Step 4: Use Equation 1 to find C
Now, we can use Equation 1 to express C in terms of A and B:
From Equation 1:
\[ A + B = 28000 \]
Substituting this into Equation 4:
\[ 28000 + C = 44000 \]
Now, solve for C:
\[ C = 44000 - 28000 = 16000 \]

### Conclusion
The monthly income of C is Rs 16,000.

---