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J completed a piece of work in 7 days, working 4 hours in a day while K completed a piece of work in 5 days working 7 hours in a day. In how many days can they together complete double of the work working 14 hours a day? 

J completed a piece of work in 7 days, working 4 hours in a day while K completed a piece of work in 5 days working 7 hours in a day. In how many days can they together complete double of the work working 14 hours a day?  Correct Answer 20/9 days

Given:

J completed a piece of work in 7 days, working 4 hours day.

K completed a piece of work in 5 days working 7 hours a day.

J and K together worked for 14 hours a day.

Concepts used:

1 day's work done by an individual = Work/time

Time = Work/Efficiency

Calculation:

Time taken by J to complete the work in hours = 7 × 4 = 28 hours 

Time taken by K to complete the work in hours = 7 × 5 = 35 hours 

1 hour work done by individual = Work/time

⇒ 1 hour work of J = 1/(7 × 4) = 1/28

⇒ 1 hour work of K = 1/(5 × 7) = 1/35

⇒ 1 day, 1 hour work of J and K = (1/28) + (1/35) = 9/140

1 day, 14 hours work of J and K = 14 × 9/140 = 9/10

Time = Work/Efficiency

Time taken by J and K in completing twice the full work = 2/(9/10) days = 20/9 days

∴ Working 14 hours a day, J and K took 20/9 days in completing double the piece of work. 

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