P and Q can harvest a field in 5 and 7 days respectively.after P has worked for 3 days, he is joined by Q.in how many more days will the work be completed?

P`s one day work =

Q`s one day work =

Since P worked alone for 3 days,

work completed by P =

Work left =

Now, Q also joined P.

So, work done by them in one day = P`s one day work + Q`s one day work

=

So, of work is completed in 1 day

so, of work will be completed in

Hence, the work will be completed on the second day when they start working together.

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HARVESTING COMPLETED BY P IN 5DAYS

HARVESTING COMPLETED  BY Q IN 7 DAYS

SO WORK DONE BY P IN ONE DAY= 1/5

AND Q = 1/7

NOW WORK DONE BY P IN  3 DAYS = 3/5

NOW TOTAL WORK DONE BY THEM IN ONE DAY = 1/5+1/7

  =  7+5/35

  =  12/35

  SO DAYS NEDDE TO COMPLETE  THE HARVEST=35/12 DAYS

AS WE KNOW THAT  3/5 PART OF WORK HAS BEEN ALREADY DONE BY P 

SO NOW TIME TAKEN TO COMPLETE THE HARVEST = 35/12 - 3/5

  = 175-36/60

  = 139 / 60 DAYS

  =  2 19/60  DAYS

SO TIME TAKEN TO COMPLETE THE HARVEST IS 2  19/60 DAYS

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