Staggered teamwork and fair pay: A can finish a job in 20 days. After A works alone for 5 days, B joins and together they finish in the next 10 days. If they are paid ₹ 1600 in total, what is the fair payment to A and to B?

Introduction / Context:
When workers join at different times, the proper division of payment uses the actual fraction of work each one completes. Compute each worker’s contribution from their rates and the periods they worked, then split the total payment in that ratio.

Given Data / Assumptions:

• A alone can finish in 20 days ⇒ A’s rate = 1/20 job/day.
• A works alone for 5 days, then A and B work together for 10 more days.
• Total payment = ₹ 1600; shares proportional to work done.

Concept / Approach:
Find the combined rate during the last 10 days from the fact that the total job is completed in 15 days. From that, extract B’s rate. Then compute A’s total contribution (first 5 days alone plus A’s share during the joint 10 days) and B’s contribution. Divide ₹ 1600 in that ratio.

Step-by-Step Solution:

Verification / Alternative check:
A:B = 3:1 indeed sums to ₹ 1600 and matches computed contributions.

Why Other Options Are Wrong:
Other splits do not reflect the 3:1 work division. “None” is unnecessary because the correct split is determinable.

Common Pitfalls:
Dividing payment by time spent together only, ignoring A’s solo work; or assuming equal split during the joint period without considering rates.

Final Answer:
₹ 1200 to A, ₹ 400 to B