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# Arithmetic Aptitude :: Time and Work

## 7. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?

Explanation :

X one day work = 1/20

y one day work = 1/12

work done by x in 4 days = 4 * 1/20 = 1/5
left work = (1-1/5) = 4/5

x and y one day work = (1/20 + 1/12) = 8/60 = 2/15
=> time required to do 2/15 part of work by x and y = 1 day
so for whole work = 1/(2/15) = 15/2
so for 4/5 part of work x and y will take =( 4/5*15/2 ) = 6 days.
=> How long did the work last = 4 day + 6 day = 10 days.