Work and Wages – Share by work rate when working together: A completes the work alone in 9 days; B alone in 15 days. If they work together and split wages proportional to contribution, what is the ratio A : B?

Introduction / Context:
With constant rates, the share of wages for each worker equals the share of total work done, i.e., the worker’s rate compared to the team’s rate. This is a straightforward ratio of reciprocals of the individual times.

Given Data / Assumptions:

• A’s time = 9 days ⇒ rate = 1/9
• B’s time = 15 days ⇒ rate = 1/15

Concept / Approach:
Wage ratio A:B = (1/9):(1/15) = 15:9, which simplifies to 5:3. This uses the principle that faster worker receives proportionally more.

Step-by-Step Solution:
(1/9):(1/15) = 15:9Simplify ⇒ 5:3

Verification / Alternative check:
Use 45-unit model: A does 5 units/day, B does 3 units/day, so shares 5:3.

Why Other Options Are Wrong:
3:5 reverses the correct order; others do not reduce from 15:9.

Common Pitfalls:
Dividing by days directly; remember rates (reciprocals) determine shares.

Final Answer:
5 : 3