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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: 0.12 P + 0.14 (1.5 P) = 0.12 P + 0.21 P = 0.33 P = 792.P = 792 / 0.33 = 2400; Q = 1.5 * 2400 = 3600.Total = 2400 + 3600 = ₹ 6000. Verification / Alternative check: Interest check: 2400*0.12 + 3600*0.14 = 288 + 504 = 792 (over 2 years combined factors already applied). 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.

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.

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