A, B and C can complete a work in 20, 24 and 30 days respec tively. All of them starts to gether but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?

LCM of 20,24 and 30 is 120 unit (required work)
A's 1-day work 120/20 = 6 unit per day
B's 1-day work 120/24 = 5 unit per day
C's 1-day work 120/30 = 4 unit per day
A+B+C =15 unit per day, work for 4 day = 15*4= 60,
left work 120-60=60unit
now A leaves and B will leave 6 before work completed and the rest work is done by C
let C takes t day's to finish the after A leave then
C work done = 4*t and B's work done 5(t-6)
4*t + 5(t-6) = 60
on solving we get, t= 10
Total days 10+4=14