A, b,c can do a work in 24,30,40 days. They start work together but c leaves 4 days before the completion of the work. In how many days is the work done?
Answers
Answer:
11 1/3 days are needed to complete the work.
Step-by-step explanation:
A can do a work in 24 days
So A's one day work = 1/24
B can do the same work in 30 days
So B's one day work = 1/30
C can do the same work in 40 days
So C's one day work = 1/40
(A,B and C)'s one day work = 1/24 + 1/30 + 1/40
= (5 + 4 + 3)/120
= 12/120
= 1/10
So A,B,C together can do a work in 10 days
Number of days A,B,C work together = 10 - 4
= 6 days
Work done by A,B,C in 6 days = 6 * 1/10 = 6/10
Remaining work that is to be done A and B alone = 1 - 6/10
= 1/1 - 6/10
= (10 - 6)/10
= 4/10
(A and B)'s one day work = 1/24 + 1/30
= (5 + 4)/120
= 9/120
= 3/40
So 1 work A, B do in = 40/3 days
4/10 work A,B do in = 40/3 * 4/10
= 4/3 * 4
= 16/3 days
Total number of days = 6 + 16/3
= 6/1 + 16/3
= (18 + 16)/3
= 34/3
= 11 1/3 days
Therefore 11 1/3 days are needed to complete the work.