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Working for 9 hours a day, X can finish a task in 3 days, Y can finish three times of the same task in 8 days, and Z can finish five times of the same task in 12 days. Working together, in how many hours will they complete the task?

Working for 9 hours a day, X can finish a task in 3 days, Y can finish three times of the same task in 8 days, and Z can finish five times of the same task in 12 days. Working together, in how many hours will they complete the task? Correct Answer 8

Given:

Working hours a day = 9 hours

Number of day X work to complete task = 3 days

Number of days Y work to complete three times of same task = 8 days

Number of days Z work to complete five times of same task = 12 days

Concept Used:

Total work = Number of working days × Efficiency

Calculation:

Total number of working hours of X = 3 × 9 = 27 hours

Total number of working hours of Y = 8/3 × 9 = 24 hours

Total number of working hours of Z = 12/5 × 9 = 108/5 hours

Taking LCM of X, Y, Z (27, 24, 108/5) = 1080 units

Efficiency of X = 1080/27 = 40

Efficiency of Y = 1080/24 = 45

Efficiency of Z = 1080/(108/5) = 50

Total efficiency of X + Y + Z = 135

Total work = Number of working days × Efficiency

Number of Days all together to complete the same work = 1080/135 = 8 hours

 ∴ In 8 hours they will complete the task working together.

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