Simple Interest — Two sums at 6% and 7% with a linking condition: A man invests one sum at 6% p.a. SI and another at 7% p.a. SI. In 2 years, the combined interest is ₹ 792. Also, half of the first sum equals one-third of the second sum. Find the total sum invested.

Introduction / Context:
Multiple investments with a relationship between principals can be solved by converting the relation into a single variable and using the total interest condition under SI. This avoids solving a full two-variable system from scratch.

Given Data / Assumptions:

• P at 6% p.a., Q at 7% p.a., both for 2 years
• Total interest in 2 years = ₹ 792
• (1/2) P = (1/3) Q ⇒ Q = (3/2) P

Concept / Approach:
Total SI = P * 0.06 * 2 + Q * 0.07 * 2 = 0.12 P + 0.14 Q. Substitute Q = 1.5 P to get a single equation in P; then compute Q and P + Q.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 5800, 5900, 6100, 6200 do not satisfy both the interest total and the linkage.

Common Pitfalls:

• Mistaking (1/2)P = (1/3)Q into Q = (2/3)P; correct is Q = (3/2)P.

Final Answer:
₹ 6000.