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A can do a piece of work in 14 days and B in 21 days They begin the work together but 3 days before the completion of work A leaves The work was completed in?
'A' does (1/14) of the job in 1 day. 'B' does (1/21) of the job in 1 day.
'B' worked alone for the last 3 days. In that time, he did the last (3/21) of the job.
So the part they did together was the first (18/21) of the total job.
Working together, they do (1/14 + 1/21) = (3/42 + 2/42) = (5/42) of the job each day.
If the number of days they worked together was 'D', then (5/42)D = (18/21).
D = (18/21) / (5/42) = (18/21) x (42/5) = (18 x 42 / 21 x 5) = 36/5 = 7.2 days.
They worked together for 7.2 days. Then 'A' left. and 'B' worked alone for 3 days.
The work was completed in (7.2 + 3) = 10.2 days.
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Check:
[ (7.2) x (5/42) ] + (3/21) = (36/42) + (3/21) = (36/42) + (6/42) = (42/42) = 1 job yay!
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