In a partnership business, Vishal invests 10% more than Trishul, and Trishul invests 10% less than Raghu. If the total of their investments is Rs. 5780, how much amount does Raghu invest?

Introduction / Context:
This aptitude question is based on the concept of partnership and percentage increase and decrease in investments. The aim is to calculate Raghu's original investment when the total amount invested by three people, Vishal, Trishul and Raghu, is known and their investments are linked through percentage relations.

Given Data / Assumptions:

• Raghu invests an amount R (in rupees).
• Trishul invests 10% less than Raghu, that is 0.9R.
• Vishal invests 10% more than Trishul, that is 1.1 times Trishul's amount.
• Total investment of all three partners is Rs. 5780.
• All three investments are made for the same period, so only capital amounts matter.

Concept / Approach:
The key ideas are percentage increase and decrease applied in sequence and then forming a simple linear equation. When one person invests 10% less than another, the factor is 0.9. When someone invests 10% more than another amount, the factor is 1.1. By expressing all three investments in terms of Raghu's amount R, we can write the total as a single equation and solve for R. This is a standard partnership and percentage mixture problem often asked in competitive exams to test comfort with basic algebra and percentages.

Step-by-Step Solution:
Step 1: Let Raghu's investment be R rupees. Step 2: Trishul invests 10% less than Raghu, so Trishul's amount is 0.9R. Step 3: Vishal invests 10% more than Trishul, so Vishal's amount is 1.1 * 0.9R = 0.99R. Step 4: Total investment is R + 0.9R + 0.99R = 2.89R. Step 5: Given that the total is Rs. 5780, set up the equation 2.89R = 5780. Step 6: Solve for R using division: R = 5780 / 2.89 = 2000. Step 7: Therefore, Raghu invests Rs. 2000.

Verification / Alternative check:
To verify the result, recalculate individual contributions using R = 2000. Trishul invests 10% less than 2000, which is 0.9 * 2000 = 1800. Vishal invests 10% more than 1800, that is 1.1 * 1800 = 1980. Now add all three amounts: 2000 + 1800 + 1980 = 5780. This matches the given total sum exactly, so the computed value of Raghu's investment is consistent and correct.

Why Other Options Are Wrong:
Rs. 2010, Rs. 2100 and Rs. 2200 give totals that do not add up to Rs. 5780 when the same percentage rules are applied. For example, if Raghu invested Rs. 2100, then Trishul would invest 10% less, which is 1890, and Vishal would invest 10% more than 1890, which is 2079. The total would then be 2100 + 1890 + 2079 = 6069, which is not equal to Rs. 5780. The option Rs. 1900 similarly fails to produce the correct total.

Common Pitfalls:
A common mistake is to treat the 10% increase and 10% decrease as cancelling each other directly, which they do not, because they are applied on different base amounts. Another frequent error is to misread the statement and think Vishal invests 10% more than Raghu instead of 10% more than Trishul. Candidates may also forget to convert percentages into decimal multipliers correctly, leading to incorrect equations. Keeping track of who is more or less than whom is essential in partnership questions like this.

Final Answer:
Raghu's investment is therefore Rs. 2000, which matches option C.