Linking successive percentage relations in investments: Sonu invested 10% more than Mona, and Mona invested 10% less than Raghu. If their combined investment is ₹ 5,780, find Raghu’s investment.

Introduction / Context:
This is a chained-percentage linkage problem. Express each person’s investment in terms of Raghu’s base amount R. Then sum the three expressions, set equal to the given total, and solve for R. Percentage increases/decreases convert directly to multipliers (1.10 for +10%, 0.90 for −10%).

Given Data / Assumptions:

• Mona = 10% less than Raghu ⇒ Mona = 0.9R.
• Sonu = 10% more than Mona ⇒ Sonu = 1.1 * Mona = 1.1 * 0.9R = 0.99R.
• Total = Sonu + Mona + Raghu = ₹ 5,780.

Concept / Approach:
Replace all amounts with R expressions and solve a single linear equation in R. This avoids guesswork and ensures consistency with both percentage statements.

Step-by-Step Solution:

Verification / Alternative check:
Mona = 0.9*2,000 = ₹ 1,800; Sonu = 0.99*2,000 = ₹ 1,980. Sum = 1,980 + 1,800 + 2,000 = ₹ 5,780, exactly the given total.

Why Other Options Are Wrong:
₹ 2,100, ₹ 2,010, ₹ 2,210, ₹ 1,990 fail to satisfy both chained percentage conditions when recomputed and summed to ₹ 5,780.

Common Pitfalls:
Applying +10% to Raghu directly for Sonu, or combining percentages additively (10% − 10% = 0%) instead of multiplicatively (1.1 * 0.9 = 0.99).

Final Answer:
₹ 2000