'Amit' can complete a project in 20 days while 'Bhavya' can do it in 30 days alone. Bhavya starts the project on Day 1, then Amit works on Day 2, and both work together on Day 3. They follow this sequence repeatedly. How many days will they take to complete the project?

ATQ,

Let the total work be LCM (20, 30) = 60 units

Efficiency of Amit = 60 / 20 = 3 units/day

Efficiency of Bhavya = 60 / 30 = 2 units/day

Work done in 3 days = Bhavya (2×1) + Amit (3×1) + Both (5×1) = 2 + 3 + 5 = 10 units

In 3×5 = 15 days (5 full cycles), work = 10 × 5 = 50 units

Remaining work = 60 - 50 = 10 units

Next 2 days work = Bhavya (2) + Amit (3) = 5 units

Remaining = 10 - 5 = 5 units

Next day (both) do 5 units → full day

Total time = 15 (full cycles) + 2 + 1 = 18 days