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A and B can complete a piece of work together in 20 days. They start work together but A had to leave 5 days before the work finally got over. If B finishes the remaining in 18 days, then how long will B take to complete the work separately.
1. 72 days
2. 64 days
3. 100 days
4. 120 days

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Correct Answer - Option 1 : 72 days

∵ A left before 5 days due to which B had to work for 18 days

⇒ 5-day work of A and B together = 18 days work of B

Let the efficiency of A and B be x and y respectively

5 (x + y) = 18y

⇒ 5x + 5y = 18y

⇒ 5x = 13y

⇒ x : y = 13 : 5

Total work = (13 + 5) × 20 = 360 units

∴ Time taken by B alone to complete the work = 360/5 = 72 days

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