Classic Pair-Work Problem A can do a piece of work in 10 days and B can do it in 15 days. If they work together from start to finish, in how many days will they complete the work?

Introduction / Context:
This is a standard two-person time-and-work problem. The trick is to add the rates (reciprocals of the times) and invert to find the combined duration.

Given Data / Assumptions:

• A: 10 days ⇒ 1/10 per day.
• B: 15 days ⇒ 1/15 per day.

Concept / Approach:
Combined rate r = 1/10 + 1/15 = (3 + 2)/30 = 5/30 = 1/6. Total time = 1/r = 6 days.

Step-by-Step Solution:
r = 1/10 + 1/15 = 1/6 job/dayTime = 1 / (1/6) = 6 days

Verification / Alternative check:
If they complete 1/6 per day together, in 6 days they finish the job, matching the calculation.

Why Other Options Are Wrong:
8, 9, 10, and 12 days are inconsistent with the derived combined rate of 1/6 per day.

Common Pitfalls:
Using the average of 10 and 15 instead of the reciprocal-sum method.

Final Answer:
6