A and B can complete a piece of work in 8 and 10 days respectively However they work alternately one day each with beginning the work In how much time will the work be completed?
With WHO beginning the work? Person A? You seem to have left out a letter.
Assume A starts the job. After 1 day it will be 1/8 complete. After 8 days is will be 4/8 + 4/10 = 9/10 complete, and it will be A's turn again. The job will be completed near the end the ninth day.
To find out how much time it will take for A and B to complete the work, we need to calculate how much work they can do in one day.
Let's first calculate A's efficiency. A can complete the work in 8 days, so in one day, A can complete 1/8th of the work. Similarly, B can complete 1/10th of the work in one day.
Since A and B work alternately, they will work for a total of (8 + 10) = 18 days.
Now, let's calculate how much work they will complete in one day working alternately:
On day 1, A completes 1/8th of the work.
On day 2, B completes 1/10th of the remaining work (since A already completed 1/8th).
On day 3, A completes 1/8th of the remaining work (since B already completed 1/10th).
And so on...
We can see that on even-numbered days (starting from day 2), B completes 1/10th of the remaining work, and on odd-numbered days (starting from day 1), A completes 1/8th of the remaining work.
Let's calculate the total work done in each pair of alternating days:
- On days 1 and 2, A and B complete a total of (1/8 + 1/10) = 9/40th of the work.
- On days 3 and 4, A and B complete a total of (1/8 + 1/10) = 9/40th of the remaining work.
- And so on...
We can see that A and B complete a total of 9/40th of the remaining work in every two consecutive days.
Since there are 18 days in total, we can divide 18 by 2 to find out how many pairs of alternating days there are and multiply that by 9/40 to get the total work completed.
(18/2) * (9/40) = 9/4 = 2 1/4
Therefore, A and B will complete the work in 2 and 1/4th days.