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A can complete a plastic puzzle in 4 hours while B can destroy the same puzzle in 6 hours. If both A and B work together for 7 hours after which B left, how much time is taken by A to complete the remaining puzzle?

A can complete a plastic puzzle in 4 hours while B can destroy the same puzzle in 6 hours. If both A and B work together for 7 hours after which B left, how much time is taken by A to complete the remaining puzzle? Correct Answer 1 hour 40 minutes

Given:

A can complete a plastic puzzle in 4 hours while B can destroy the same puzzle in 6 hours.

Both A and B work together for 7 hours after which B left.

Concepts used:

Time = Work/Efficiency

1 hour work of individual = Work/Time

Calculation:

1 hour work of A = ¼

1 hour work of B = -1/6

Both A and B work together for 7 hours after which B left.

⇒ 1 hour work of A and B = ¼ - (1/6) = 1/12

⇒ 7 hours work of A and B = 7/12 

Remaining puzzle to be completed by A = 1 – (7/12) = 5/12    

⇒ Time taken by A to complete remaining puzzle = Work/Efficiency = 5/12/1/4 = 5/3 hours = 1 hour 40 minutes

∴ A took 1 hour 40 minutes to complete the remaining puzzle.

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