Three workers with partial contribution: A can complete a job in 12 days and B can complete it in 15 days. A and B work together for 5 days; the remaining work is done by C alone. If the total wage paid is ₹ 720, what is B's share?

Introduction / Context:
This problem distributes a fixed payment according to the actual fraction of work completed by each participant. A and B work together for a fixed time; C finishes the remainder. We compute each contribution and then split ₹ 720 proportionally.

Given Data / Assumptions:

• Total job = 1 unit
• Rate(A) = 1/12, Rate(B) = 1/15
• Joint work by A and B for 5 days
• Remaining work is done by C
• Total payment = ₹ 720

Concept / Approach:
Find work completed by A and B in 5 days; the leftover is C's portion. Convert each portion into money by multiplying each fraction by ₹ 720. B's share is requested.

Step-by-Step Solution:
Work by A in 5 days = 5 * (1/12) = 5/12Work by B in 5 days = 5 * (1/15) = 1/3Total done by A+B = 5/12 + 1/3 = 5/12 + 4/12 = 3/4Remaining = 1 − 3/4 = 1/4 ⇒ C's workB's share = (1/3) * 720 = ₹ 240

Verification / Alternative check:
Convert all shares to money: A = (5/12)*720 = ₹ 300; B = ₹ 240; C = (1/4)*720 = ₹ 180. Sum = ₹ 720 (consistent).

Why Other Options Are Wrong:
₹ 95, ₹ 100, ₹ 104 are far below the proportion 1/3 of ₹ 720.

Common Pitfalls:
Allocating by days rather than by work; forgetting that C's share is solely the leftover portion after A and B's combined effort.

Final Answer:
₹ 240