Acan do a piece of work in 14 days while B can do in 21 days they begin together but 3 days before the completion of the work A leaves off. final total number of days taken to complete the work
Answers
Let the total no. of days needed to complete the work be x days.
Let's assume total work to be 1.
1 day work of A = 1/14 part
1 day work of B = 1/21 part
Since A leaves 3 days before completion of work, therefore A works for (x-3) days.
And B works for x days.
According to the question,
(1/4)×(x-3)+(1/21)×x=1
3x-9+2x=42
5x=51
x=10.2 days.
So total days needed to complete the work = 10.2 days.
Acan do a piece of work in 14 days
while B can do in 21 days
Efficiency of A = 1/14.
Efficiency of B = 1/21.
Amount of work completed by B in 3 days = 3/21. I.e. 1/7
The remaining work was done by A and B together.
Therefore, remaining work = 1–(1/7) = 6/7.
Total work is taken as 1 in this case.
Therefore, combined efficiency=(1/14)+(1/21).
Combined efficiency = 5/42
Therefore number of days A and B worked together is given as,
(5/42)x = 6/7.
We get x = 7.2 days
Therefore total days to complete the work = 10.2 days.