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If A, B and C can do a task working alone in 12, 18 and 36 days respectively. They all work together for 2 days, then B quits. How many days A and C working together will take to complete the remainder of the task?

If A, B and C can do a task working alone in 12, 18 and 36 days respectively. They all work together for 2 days, then B quits. How many days A and C working together will take to complete the remainder of the task? Correct Answer 6

A can do a task in = 12 day

∴ A’s 1 day’s task = 1/12

B can do a task in = 18 day

∴ B’s 1 day’s task = 1/18

C can do a task in = 36 day

∴ C’s 1 day’s task = 1/36

Let, A and C will take x days to complete the remainder of the task

According to the question,

⇒ (x + 2) × 1/12 + 2/18 + (x + 2) × 1/36 = 1

⇒ x/12 + 1/6 + 1/9 + x/36 + 1/18 = 1

⇒ (3x + x)/36 = 1 - (3 + 2 + 1)/18

⇒ x/9 = 1 - 1/3

⇒ x/9 = 2/3

⇒ x = 6

∴ A and C will take 6 days to complete the remainder of the task.

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