Rs. 680 is divided among A, B, and C. It is known that A gets two-thirds of B’s share, and B gets one-fourth of C’s share. What is B’s share?

Introduction / Context:
The statement links each person’s share multiplicatively. The cleanest method is to express all shares in terms of a single variable, typically C, then enforce the total sum to get numerical values.

Given Data / Assumptions:

• A = (2/3)B
• B = (1/4)C
• A + B + C = 680

Concept / Approach:
Write everything in terms of C. Then compute the total as a multiple of C, solve for C, and back-calculate B. This avoids fractional tangle and ensures consistency.

Step-by-Step Solution:
B = C/4A = (2/3) * (C/4) = C/6Total = C/6 + C/4 + C = (2/12 + 3/12 + 12/12)C = (17/12)C(17/12)C = 680 ⇒ C = 680 * 12 / 17 = 480B = C/4 = 480/4 = 120

Verification / Alternative check:
Compute A = C/6 = 80, then A + B + C = 80 + 120 + 480 = 680 matches. Also A = (2/3)B = 80 (correct) and B = (1/4)C = 120 (correct).

Why Other Options Are Wrong:
60, 80, 160, and 140 do not satisfy all three conditions simultaneously when checked.

Common Pitfalls:
Misreading the statement as A equals two-thirds of (B plus something), or treating “one-fourth of C” as C minus one-fourth. Keep it multiplicative.

Final Answer:
Rs. 120