A person divides ₹17,200 into three parts and invests them at simple interest rates of 5%, 6%, and 9% per annum respectively. At the end of 2 years, the simple interest earned on each part is the same. What is the amount (in rupees) invested at 9% per annum?

Introduction:
This question tests proportional allocation of principal across multiple simple interest rates when the interest earned is the same for each part. Because all investments run for the same time (2 years), equal interest implies the principals are inversely proportional to the rates. This is a common aptitude pattern: equal SI at different rates means higher rate gets smaller principal.

Given Data / Assumptions:

• Total sum = ₹17,200
• Rates: 5%, 6%, 9% per annum
• Time = 2 years for each part
• Simple interest on each part after 2 years is equal (say I rupees)
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Let the common interest (for 2 years) be I for each part. Then for each rate r, principal P = (I * 100) / (r * t). With t = 2, this becomes P = (50I)/r. Express each principal in terms of I, add them to equal ₹17,200, solve for I, then compute the 9% principal.

Step-by-Step Solution:
P5 = (50I)/5 = 10I P6 = (50I)/6 = 25I/3 P9 = (50I)/9 Total: 10I + 25I/3 + 50I/9 = 17200 Convert to denominator 9: (90I/9) + (75I/9) + (50I/9) = 17200 (215I/9) = 17200 => I = 17200*9/215 = 720 P9 = (50*720)/9 = 4000

Verification / Alternative check:
If P9=4000, SI in 2 years at 9% is (4000*9*2)/100 = 720. Then P5 must be 8000 (SI=720) and P6 must be 5200 (SI=720). Total = 8000+5200+4000 = 17200, correct.

Why Other Options Are Wrong:
Other values do not allow the 5% and 6% parts to adjust to the same 2-year interest while still summing to ₹17,200.

Common Pitfalls:
Forgetting to include the 2-year time factor, using direct proportionality instead of inverse proportionality, or assuming equal principal instead of equal interest.

Final Answer:
The amount invested at 9% per annum is ₹4,000.