Simple Interest — Mixed fractions of a fund at different rates: One-third of a sum is at 3% p.a., one-sixth at 6% p.a., and the rest at 8% p.a. If total SI for 2 years is ₹ 600, find the original sum.

Introduction / Context:
This is a weighted-average SI problem across sub-parts of one principal. Each fraction contributes SI proportional to its share, rate, and time; the total is the sum of these contributions over 2 years.

Given Data / Assumptions:

• Total principal S (unknown)
• 1/3 at 3% p.a.; 1/6 at 6% p.a.; remainder at 8% p.a.
• Time = 2 years; total SI = ₹ 600

Concept / Approach:
Total SI = S * [ (1/3)*0.03*2 + (1/6)*0.06*2 + (1 − 1/3 − 1/6)*0.08*2 ]. Evaluate the bracket and equate to 600 to solve for S.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other sums do not satisfy the 0.12 * S = 600 condition.

Common Pitfalls:

• Forgetting that the leftover fraction is 1 − 1/3 − 1/6 = 1/2.

Final Answer:
₹ 5000.