A, B, and C can complete a certain task in 20, 30, and 60 days respectively. How many days will it take for A to finish the work if he receives help from B and C every third day?
15 days
Step 1 — total work in convenient units. Take total work = LCM\((20,30,60) = 60\) units.
Then daily efficiencies are \(60/20 = 3,\; 60/30 = 2,\; 60/60 = 1\) units/day for A, B, C.
Step 2 — work pattern over each 3-day cycle:
Day 1: A alone → 3 units. Day 2: A alone → 3 units. Day 3: A+B+C → \(3+2+1 = 6\) units.
Total per 3-day cycle = \(3 + 3 + 6 = 12\) units.
Step 3 — number of cycles:
\(\dfrac{60}{12} = 5 \text{ cycles} \implies 5 \times 3 = 15 \text{ days}\)
Hence A finishes the job in 15 days.
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