A can complete a task in 12 days B can complete the same task in 18 days If A and B work on this sam...........

Quant (SSC) Percentage

A can complete a task in 12 days. B can complete the same task in 18 days. If A and B work on this same task on alternate days starting with A, in how many days do they finish the entire task?

11.8

14.33

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Explanation:

As per the question,
Work done by A per day = 1/12
Work done by B per day = 1/18
As A & B work on alternate days starting with A.
At the end of second day the amount of work completed would be
Work done by the end of 2nd day,
= 1/12 + 1/18 = 5/36
So, in order to complete the work this fraction has to be equal to 1.
5/36 + 5/36 +…. 7 times will be equal to 35/36 which is closest to 1.
Hence, the time taken to finish 35/36 work will be 14 days (5/36 is two days work, so 35/36 will be equal to 7 × 2 days) On the 15^thday,
A works. The work remaining is 1/36 and A can finish 1/12 of the work in 1 day.
Hence time required by A to do 1/36 work = 1/36 / 1/12 = 1/3 days
Therefore, the time taken by A & B to complete while working alternatively would be 14 + 1/3 = 14.33 days.