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A and B can complete a piece of task together in 12 days, while A alone can do it in 15 days. They start working together but A leaves 10 days before the completion of the task. For how many days did A and B work together?

A and B can complete a piece of task together in 12 days, while A alone can do it in 15 days. They start working together but A leaves 10 days before the completion of the task. For how many days did A and B work together? Correct Answer 10

Let the amount of the work = 60 units.

A and B can complete a piece of task together in 12 days,

⇒ Amount of work A and B complete in a day = 60/12 = 5 units

A alone can do it in 15 days,

⇒ Amount of work A completes in a day = 60/15 = 4 units.

⇒ Amount of work B completes in a day = 5 – 4 = 1 unit.

Assume they work together for x day, then A leaves and B works alone for 10 days.

⇒ 5(x) + 10(1) = 60

⇒ 5x = 50

⇒ x = 10

∴ For 10 days A and B work together.

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