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A, B and C can finish a task in 42 days, 84 days and 28 days, respectively. A started the work. B joined him after 3 days. If C joined them after 5 days from the beginning, then for how many days did A work till the completion of the task?

A, B and C can finish a task in 42 days, 84 days and 28 days, respectively. A started the work. B joined him after 3 days. If C joined them after 5 days from the beginning, then for how many days did A work till the completion of the task? Correct Answer 17

Let the total work be LCM (42, 84, 28) = 84

A, 42 days efficiency 2

B, 84 days efficiency 1

C, 28 days efficiency 3

Initially A work for 3 days = 3 × 2 = 6 work

A and B together work for 2 days = 3 × 2 = 6 work

Remaining work = 84 – 12 = 72

Time taken by A , B and C to complete the remaining work = 72/6 = 12 days

∴ A work for = 3 + 2 + 12 = 17 days

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