Sonu invested 10% more than the investment of Mona and Mona invested 10% less than the investment of Raghu. If the total investment of all the three persons is X 5780, find the investment of Raghu.

Options

A. X 2010
B. X 2000
C. X 2100
D. X 2210

Answer

To solve the problem step by step, we will define the investments of Sonu, Mona, and Raghu based on the information provided.

### Step 1: Define the investments
Let Raghu's investment be \( R \).
Since Mona invested 10% less than Raghu, we can express Mona's investment as:
\[ M = R - 0.1R = 0.9R \]

Sonu invested 10% more than Mona, so we can express Sonu's investment as:
\[ S = M + 0.1M = 1.1M = 1.1(0.9R) = 0.99R \]

### Step 2: Write the total investment equation
The total investment of all three persons is given as \( 5780 \). Therefore, we can write:
\[ S + M + R = 5780 \]
Substituting the expressions for \( S \) and \( M \):
\[ 0.99R + 0.9R + R = 5780 \]

### Step 3: Combine the investments
Now, combine the terms:
\[ (0.99R + 0.9R + R) = (0.99 + 0.9 + 1)R = 2.89R \]
Thus, we have:
\[ 2.89R = 5780 \]

### Step 4: Solve for Raghu's investment
To find \( R \), we divide both sides by \( 2.89 \):
\[ R = \frac{5780}{2.89} \]
Calculating this gives:
\[ R \approx 2000 \]

### Conclusion
Therefore, Raghu's investment is \( 2000 \).