The average monthly income of Rakesh and Suresh is Rs. 5050. The average monthly income of Suresh and Ramesh is Rs. 6250 and the average monthly income of Rakesh and Ramesh is Rs. 5200. What is the monthly income of Rakesh?

Options

A. 2500
B. 4000
C. 6000
D. 3000

Answer

To find the monthly income of Rakesh, we can set up the problem using the information provided about the average incomes of Rakesh, Suresh, and Ramesh.

### Step-by-step Solution:

1. **Set Up the Equations:**
- Let Rakesh's income be \( R \).
- Let Suresh's income be \( S \).
- Let Ramesh's income be \( M \).

From the problem, we have the following averages:
- The average monthly income of Rakesh and Suresh is Rs. 5050:
\[ \frac{R + S}{2} = 5050 \implies R + S = 10100 \quad \text{(Equation 1)} \]
- The average monthly income of Suresh and Ramesh is Rs. 6250:
\[ \frac{S + M}{2} = 6250 \implies S + M = 12500 \quad \text{(Equation 2)} \]
- The average monthly income of Rakesh and Ramesh is Rs. 5200:
\[ \frac{R + M}{2} = 5200 \implies R + M = 10400 \quad \text{(Equation 3)} \]

2. **Add All Equations:**
Now, we will add all three equations together:
\[ (R + S) + (S + M) + (R + M) = 10100 + 12500 + 10400 \]
Simplifying the left side:
\[ 2R + 2S + 2M = 33000 \]
Dividing the entire equation by 2:
\[ R + S + M = 16500 \quad \text{(Equation 4)} \]

3. **Find Rakesh's Income:**
Now, we can use Equation 4 and subtract Equation 2 to find Rakesh's income:
\[ R + S + M - (S + M) = 16500 - 12500 \]
This simplifies to:
\[ R = 4000 \]

### Conclusion:
The monthly income of Rakesh is Rs. 4000.