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.