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 Rs 5780, then find the investment of Raghu

Options

A. Rs 1850
B. Rs 2000
C. Rs 2200
D. Rs 2320

Answer

To solve the problem step by step, let's denote the investments of Sonu, Mona, and Raghu as S, M, and R respectively.

### Step 1: Establish Relationships
From the problem statement:
- Sonu invested 10% more than Mona:
\( S = M + 0.1M = 1.1M \)
- Mona invested 10% less than Raghu:
\( M = R - 0.1R = 0.9R \)

### Step 2: Substitute Mona's Investment in Sonu's Investment
Now, substitute the expression for M in the equation for S:
\( S = 1.1M = 1.1(0.9R) = 0.99R \)

### Step 3: Write the Total Investment Equation
The total investment of all three persons is given as Rs 5780:
\( S + M + R = 5780 \)
Substituting the expressions for S and M:
\( 0.99R + 0.9R + R = 5780 \)

### Step 4: Combine Like Terms
Combine the terms on the left side:
\( (0.99R + 0.9R + 1R) = 5780 \)
This simplifies to:
\( 2.89R = 5780 \)

### Step 5: Solve for Raghu's Investment
Now, solve for R:
\( R = \frac{5780}{2.89} \)

### Step 6: Calculate the Value
Perform the division:
\( R = 2000 \)

### Conclusion
Thus, Raghu's investment is Rs 2000.

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