Numerical answer
A can complete a piece of work in 20 days, B in 30 days and C in 60 days. A works every day. B assists A on the 1st, 3rd, 5th, … days and C assists A on the 2nd, 4th, 6th, … days. In how many days will the work be completed?
Show answer and solution
Answer: 13.25
Take total work = LCM(20, 30, 60) = 60 units. Daily rates: A = 3, B = 2, C = 1.
- Odd days (A + B): 5 units.
- Even days (A + C): 4 units.
Every 2-day cycle does 9 units. After 6 cycles (12 days): 54 units done, 6 remain.
Day 13 (odd, A + B): 5 units → 59 done, 1 unit remains.
Day 14 (even, A + C at 4 units/day): the last 1 unit takes 1/4 day.
Total = 13 + 1/4 = 13.25 days.
Trap: dividing 60 by the average rate 4.5 gives 13.33 – wrong, because the work finishes partway through an even day whose rate is 4, not 4.5.
- Odd days (A + B): 5 units.
- Even days (A + C): 4 units.
Every 2-day cycle does 9 units. After 6 cycles (12 days): 54 units done, 6 remain.
Day 13 (odd, A + B): 5 units → 59 done, 1 unit remains.
Day 14 (even, A + C at 4 units/day): the last 1 unit takes 1/4 day.
Total = 13 + 1/4 = 13.25 days.
Trap: dividing 60 by the average rate 4.5 gives 13.33 – wrong, because the work finishes partway through an even day whose rate is 4, not 4.5.
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