How to Solve Work-on-Alternate-Days Problems
Solve work-on-alternate-days aptitude problems with the cycle-rate method, a worked example, and practice questions with explanations.
Expected Interview Answer
Compute each worker's one-day work rate, sum the work done in one full two-day (or n-day) cycle when workers alternate, then divide the total job by the per-cycle work to find how many complete cycles are needed, handling the final partial day separately.
If A works on odd days and B on even days, one full cycle of 2 days completes 1/a + 1/b of the job, where a and b are each person's solo completion times. Divide the total job (1) by this cycle amount to find how many full cycles are needed; if it is not a whole number, complete the whole cycles first, then check how much of the next single day's work finishes the remaining fraction. Always track which person is working on which day of the remaining fraction, since the last, possibly partial, day could belong to either worker depending on the cycle's starting day. The key discipline is separating “whole cycles completed” from “the tail end handled day by day.”
- Per-cycle rate turns an alternating schedule into simple division
- Explicit tail-day check avoids off-by-one errors on the last day
- Generalizes cleanly to 3-way or n-way rotations, not just 2 workers
AI Mentor Explanation
Two bowlers alternating overs, one who'd take 12 overs alone to bowl out a tail and one who'd take 8, together dismiss 1/12 + 1/8 of the remaining wickets' "difficulty" every two-over cycle. Dividing the full job by that per-cycle amount tells you how many two-over cycles are needed, and then you check the next single over separately since it might belong to either bowler depending on who starts the last incomplete cycle. Alternate-day work problems use exactly this cycle-then-tail method instead of averaging the two bowlers' rates.
Worked example (alternate days)
2-day cycle rate
- 1/8 + 1/12 = 5/24
After 4 cycles (8 days)
- 4 × 5/24 = 5/6 done
Day 9 (A's turn)
- Remaining 1/6 ÷ (1/8) < 1 day
- Finishes on day 9
Step-by-Step Explanation
Step 1
Find individual daily rates
Each worker's rate is 1 ÷ their solo completion time.
Step 2
Compute the cycle rate
Sum the rates of everyone active within one full rotation.
Step 3
Count whole cycles
Divide total job (1) by the cycle rate; take the integer part.
Step 4
Resolve the tail day(s)
Apply remaining workers' rates one day at a time to the leftover fraction.
What Interviewer Expects
- Correct per-person daily rate from solo completion time
- Correctly identifies who works on which day of the rotation
- Separates whole-cycle math from the final tail-day check
- Does not assume the last day is automatically a full day's work
Common Mistakes
- Averaging the two workers' rates instead of summing per cycle
- Forgetting to check the tail day separately after whole cycles
- Misassigning which worker is active on the final partial day
- Using total combined time formulas meant for simultaneous, not alternating, work
Best Answer (HR Friendly)
“I find each person's daily work rate, add up what gets done in one full rotation cycle, and divide the whole job by that cycle rate to see how many complete cycles are needed. Then I handle whatever is left over one day at a time, checking exactly whose turn it is, rather than assuming the schedule finishes on a clean cycle boundary.”
Follow-up Questions
- How would this change with three workers rotating one day each?
- What if the workers alternate every two days instead of every one day?
- How do you handle a worker joining the rotation partway through?
- How is this different from a problem where both work simultaneously every day?
MCQ Practice
1. A can finish a job in 10 days, B in 15 days. Working on alternate days starting with A, how many days to finish?
Cycle rate = 1/10+1/15 = 1/6 per 2 days. 5 cycles (10 days) = 5/6 done. Day 11 (A) does 1/10, leaving 1/15. Day 12 (B) finishes it at rate 1/15 exactly, so 12 days.
2. Two workers alternate days; the one working on the last (partial) day should be determined by?
The rotation schedule fixes whose turn it is on any given day; you must track the cycle position, not guess.
3. A finishes a job alone in 6 days, B in 6 days, alternating days. Total time to finish?
Cycle rate = 1/6+1/6 = 1/3 per 2 days; 3 cycles (6 days) exactly completes the job.
Flash Cards
How do you compute an alternate-day cycle rate? — Sum the daily rates of every worker active within one full rotation.
How do you find the number of whole cycles? — Divide the total job (1) by the cycle rate and take the integer part.
How do you handle the leftover work? — Apply the correct next worker's single-day rate to the remaining fraction.
Common mistake in alternate-day problems? — Averaging rates instead of tracking whose turn it is each day.