A person invests a total of ₹7,900 in three different simple interest schemes offering 3%, 5%, and 8% per annum. After 1 year, the interest earned from each scheme is the same. What amount (in rupees) is invested at 3% per annum?

Introduction:
This problem tests the idea that under simple interest, for the same time (1 year here), interest depends only on principal and rate. If the interest amounts are equal across different rates, the principal amounts must be inversely proportional to the rates. That proportionality is the shortcut that makes multi-scheme split problems solvable cleanly.

Given Data / Assumptions:

• Total investment = ₹7,900
• Three rates: 3% p.a., 5% p.a., 8% p.a.
• Time = 1 year for all schemes
• Interest earned from each scheme is the same (say I rupees)
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Let the equal interest from each scheme be I. For 1 year, SI = (P * r)/100, so P = (100 * I)/r. Compute the three principals in terms of I and add them to match the total ₹7,900. Solve for I, then compute the principal at 3%.

Step-by-Step Solution:
For 3%: P3 = (100I)/3 For 5%: P5 = (100I)/5 For 8%: P8 = (100I)/8 Total: (100I)(1/3 + 1/5 + 1/8) = 7900 1/3 + 1/5 + 1/8 = (40 + 24 + 15)/120 = 79/120 (100I)*(79/120) = 7900 (7900I)/120 = 7900 => I = 120 P3 = (100*120)/3 = 4000

Verification / Alternative check:
If P3=4000, interest at 3% in 1 year is 120. Then P5 must be 2400 (5% of 2400 is 120) and P8 must be 1500 (8% of 1500 is 120). Sum = 4000+2400+1500 = 7900, correct.

Why Other Options Are Wrong:
Other values do not allow a consistent split where 3%, 5%, and 8% each yield the same interest while totaling ₹7,900.

Common Pitfalls:
Assuming equal principal instead of equal interest, forgetting to use inverse proportionality, or treating the rates as decimals while still dividing by 100.

Final Answer:
The amount invested at 3% per annum is ₹4,000.