piyali1979g wrote:
When Abel Ben and Carla started together, they finished half of the job in 2 days. So the part left is 1/2. This should be done by Ben and Carla only; and they should take 10/3 days to complete the remaining half portion, but Ben left 3 days prior to completion, that means Ben and Carla worked for only 1/3 days. In this 1/3 days Ben and Carla together finished 1/20 part, so the remaining 19/20 part of the work has to be done by the Carla alone. Carla should take 14 and 1/4 days. Hence the total duration of the work = 2+1/3+14 and 1/4 days.
Every answer so far shown here assumed that Carla should finish the job in 3 days after Ben left, but when Abel left, Ben and Carla started together, the time taken to complete the remaining job will be changed, so "T" is not fixed here. Every time "T" changes when some one leaves the job, so the answer 7 days is quite confusing.
Can any body explain with proper logic about the concept of "T" ?
Hi
piyali1979g ,
You must know, Work=Rate*Time and Total work =1
Working sequence:-
Work sequence Who worked-------Time(in no of days)=How many days?---------------Rate-------------------------Work done 1---------------- A+B+C--------------- First 2 days-----------------------------------------1/10+1/12+1/15=1/4---------2*1/4=1/2
2------------------B+C---------------------x(say)----------------------------------------------1/12+1/15---------------------x*(1/12+1/15)
3-------------------C----------------------Last 3 days--------------------------------------------1/15----------------------------3*1/15=1/5
Total work=1
So, \(\frac{1}{2}+x*(\frac{1}{12}+\frac{1}{15})+\frac{1}{5}=1\)
Or, \(x*\frac{9}{60}=\frac{1}{2}-\frac{1}{5}=\frac{3}{10}\)
Or, \(x=\frac{3}{10}*\frac{60}{9}= 2\)
So, total no of days taken by ABC to complete the work=\(2+x+3=2+2+3=7\)
_________________
Regards,
PKN
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