Question
'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?Solution
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
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