Two-worker collaboration payment: A alone completes a job in 15 days; A and B together complete it in 10 days. If the total payment is ₹ 1500, how should it be divided between A and B in proportion to their work?

Introduction / Context:
This is a standard “find B’s rate from joint rate” problem. Once each worker’s rate is known, their contributions over the same time interval can be compared, and the payment divided proportionally to those contributions for the full job completed together.

Given Data / Assumptions:

• A alone: 15 days ⇒ rate_A = 1/15.
• A + B: 10 days ⇒ rate_(A+B) = 1/10.
• Total payment = ₹ 1500; both worked simultaneously for the whole job.

Concept / Approach:
B’s rate = rate_(A+B) − rate_A = 1/10 − 1/15. Shares for the full job are proportional to rates (since the time they worked together is the same for both). Compute the ratio and split the money accordingly.

Step-by-Step Solution:

Verification / Alternative check:
The 2:1 split matches the fact that A works twice as fast as B.

Why Other Options Are Wrong:
Equal split (₹ 750 each) ignores different efficiencies; other splits do not match the 2:1 ratio.

Common Pitfalls:
Subtracting days instead of rates; always subtract rates to find the missing worker’s rate.

Final Answer:
₹ 1000 to A, ₹ 500 to B