Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 5780, how much amount did Raghu invest ?

Options

A. A) Rs.2010
B. B) Rs.2200
C. C) Rs.2000
D. D) Rs.2100

Answer

To solve the problem, let's denote the amounts invested by each person as follows:

- Let Raghu's investment be \( R \).
- Since Trishul invested 10% less than Raghu, Trishul's investment can be expressed as:
\[ T = R - 0.1R = 0.9R \]
- Vishal invested 10% more than Trishul, so Vishal's investment can be expressed as:
\[ V = T + 0.1T = 1.1T = 1.1(0.9R) = 0.99R \]

Now, we have the investments of all three individuals in terms of Raghu's investment \( R \):
- Raghu's investment: \( R \)
- Trishul's investment: \( 0.9R \)
- Vishal's investment: \( 0.99R \)

Next, we can set up the equation for the total investment:
\[ R + T + V = 5780 \]
Substituting the expressions for \( T \) and \( V \):
\[ R + 0.9R + 0.99R = 5780 \]
Combining the terms:
\[ (1 + 0.9 + 0.99)R = 5780 \]
\[ 2.89R = 5780 \]

Now, we can solve for \( R \):
\[ R = \frac{5780}{2.89} \]
Calculating this gives:
\[ R \approx 2000 \]

Thus, Raghu invested approximately Rs. 2000.

### Summary of Steps:
1. Define the investment of Raghu as \( R \).
2. Calculate Trishul's investment as \( T = 0.9R \).
3. Calculate Vishal's investment as \( V = 0.99R \).
4. Set up the equation for total investment: \( R + T + V = 5780 \).
5. Substitute \( T \) and \( V \) into the equation.
6. Combine the terms and solve for \( R \).