A, B, and C are partners. Twice A’s capital equals thrice B’s capital; B’s capital is four times C’s capital. Out of a total profit of Rs. 5,940, what is C’s share?

Introduction / Context:
We translate the relations among capitals into a simple ratio and then apply it to split the profit. No time factor is mentioned, so time is equal for all partners.

Given Data / Assumptions:

• 2A = 3B ⇒ A = 3B/2.
• B = 4C.
• Total profit = Rs. 5,940.

Concept / Approach:
Express A and B in terms of C and form the ratio A : B : C. Then C’s share = (C’s part / total parts) * total profit.

Step-by-Step Solution:
B = 4C. A = 3B/2 = 3*(4C)/2 = 6C. So A : B : C = 6C : 4C : C = 6 : 4 : 1. Total parts = 6 + 4 + 1 = 11. C’s share = (1/11) * 5,940 = Rs. 540.

Verification / Alternative check:
Shares = Rs. 3,240 (A), Rs. 2,160 (B), Rs. 540 (C) sum to Rs. 5,940, matching the total.

Why Other Options Are Wrong:
Rs. 700 and Rs. 900 exceed the 1/11 part. Rs. 740 is not a clean 1/11 fraction of 5,940.

Common Pitfalls:
Misreading “twice equals thrice” and solving as A = 2B/3 instead of A = 3B/2, or forgetting to reduce to the simplest A : B : C ratio.

Final Answer:
Rs. 540