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?
Correct Answer: 43/3 days
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:
Per 2 days, work = 5/36After 14 days (7 cycles), work = 7 * 5/36 = 35/36Remaining = 1 − 35/36 = 1/36Next day would be A’s day; A’s rate = 1/12Time needed = (1/36) / (1/12) = 1/3 dayTotal time = 14 + 1/3 = 43/3 daysVerification / 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