Question
A man, a woman, a boy, and a girl can complete a certain task individually in 84 days, 105 days, 140 days, and 210 days respectively. How long will it take for all four of them working together to complete the task?
Solution
Let the total work = L.C.M of 84, 105, 140, and 210 = 420 units
Efficiency of a man = 420 ÷ 84 = 5 units/day
Efficiency of a woman = 420 ÷ 105 = 4 units/day
Efficiency of a boy = 420 ÷ 140 = 3 units/day
Efficiency of a girl = 420 ÷ 210 = 2 units/day
So, time taken by a man, a woman, a boy and a girl working together = 420 ÷ (5 + 4 + 3 + 2) = 30 days
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