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A and B work alternately every hour. A can complete work in 6 hours while B can complete same piece of work in 8 hours. If work is started by A, find the time taken in completing whole piece of work if A and B work together. 


1. 26/5 hours
2. 27/4 hours
3. 35/8 hours
4. 40/9 hours

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Correct Answer - Option 2 : 27/4 hours

Given:

A and B work alternately every hour.

A can complete work in 6 hours while B can complete same piece of work in 8 hours. Work is started by A.

Concepts used:

Time = Work/Efficiency

1 hour work of individual = Work/Time

Calculation:

A can complete work in 6 hours while B can complete same piece of work in 8 hours.

1 hour work of A = 1/6

1 hour work of B = 1/8 

Work is started by A with A and B doing the work every alternate hour.

⇒ 2 hours work of A and B = (1/6) + (1/8) = 7/24

2 hours work → 7/24

6 hours work = 3 × 7/24 = 21/24

Remaining work = 1 – (21/24) = 1/8

⇒ Time taken by A to complete 1/8 piece of work = 1/8/1/6 = 3/4 hours

⇒ Total time taken by A and B to complete work = 6 hours + 3/4 hours = 27/4 hours

∴ A and B working alternately complete the work in 27/4 hours.

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