A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works every day and is assisted by B and C on every third day, in how many days is the work completed?

Problem restatementA works daily; on each third day, B and C also join for that one day. Determine total completion time.

Given data

• A: 20 days ⇒ 1÷20 per day
• B: 30 days ⇒ 1÷30 per day
• C: 60 days ⇒ 1÷60 per day

Concept/ApproachConsider a 3-day cycle: Day 1 and Day 2 (A alone), Day 3 (A + B + C). Compute work per cycle, then the number of cycles.

Step-by-step calculationWork in 2 days by A = 2 × 1÷20 = 1÷10Work on the 3rd day by A + B + C = 1÷20 + 1÷30 + 1÷60 = 1÷10Total per 3-day cycle = 1÷10 + 1÷10 = 1÷5To finish 1 unit: need 5 cycles ⇒ 5 × 3 = 15 days

Verification/Alternative1÷5 per cycle over 5 cycles totals 1.

Common pitfallsMisinterpreting “every third day” as “three days in a row.” It means only the 3rd, 6th, 9th, … days.

Final Answer15 days