A can do a work in 16 days and B can do it in 24 days. They started work together but A left 2 days before completion of the work. In how much time was the work completed?
Answers
Answer :-
Work will be completed in 12.6 days
Solution :-
A can do a work in 16 days
So A's one day work = 1/16
B can do the same work in 24 days
So B's one day work = 1/24
A and B one day work = A's one day work + B's one day work
= 1/16 + 1/24
= (3 + 2)/48
= 5/48
So A and B can do the work in 48/5 days
Number of days A and B work together = 48/5 - 2
Since A leaves 2 days before completion of work
= 48/5 - 2/1
= (48 - 10)/5
= 38/5 days
Work done by both in 38/5 days = A and B one day work * Number of days A and B work together
= 5/48(38/5)
= 1/48 * 38
= 38/48
Remaining work to be done by B = 1 - 38/48
= 1/1 - 38/48
= (48 - 38)/48
= 10/48
1 work B can do in = 24 days
10/48 work B can do in = 24 * 10/48
= 1 * 10/2
= 10/2
= 5 days
Total number of days required for completion of work = Number of days A and B work together + Number of days B required to do remaining work
= 38/5 + 5
= 38/5 + 5/1
= (38 + 25)/5
= 63/5
= 12.6 days
Therefore work will be completed in 12.6 days