Alternate-day working starting with the faster worker A and B can complete a job in 12 days and 18 days respectively. They work on alternate days, starting with A. In how many days will the entire job be finished?

Introduction / Context:
Alternate-day problems require computing the net work in 2-day cycles and then accounting for any leftover fraction with the worker who goes next.

Given Data / Assumptions:

• A alone: 12 days ⇒ 1/12 per day.
• B alone: 18 days ⇒ 1/18 per day.
• They start with A and alternate daily.

Concept / Approach:
Work per 2-day cycle = 1/12 + 1/18 = 5/36. After as many full cycles as possible, compute the remaining fraction and finish with the correct person.

Step-by-Step Solution:

Verification / Alternative check:
Numerically, 43/3 ≈ 14.33 days. This fits between 14 and 15 as expected.

Why Other Options Are Wrong:
14 and 15 days assume whole cycles; 29/2 = 14.5 is not the exact leftover computed with A’s rate.

Common Pitfalls:
Assuming an integer number of cycles or assigning the last fraction to the wrong person.

Final Answer:
43/3 days