Question

2. A can do a piece of work in 10 days and B in 20 days. They begin together but after

A leaves 2 days before the completion of the work. In how many days will the

whole work be completed?​

Answer 1

Step-by-step explanation:

A can do a piece of work in 10 days, so A’s daily capacity is 1/10 part of the work.

B can do the same work in 20 days, so Bs daily capacity is 1/20 part of the work or exactly Half of A.

Both started together and their joint capacity was …

1/10 + 1/20 = 3/20 parts Daily of the Whole Work. It means both could have completed the work in 1/(3/20) = 20/3 days. It means 6 and 2/3 days or in terms of Number of Days, technically it should be 7 days.

And when You say A left the work 2 days before Completion of the work that implies that A worked jointly with B for 5 days and had completed 1/2 the work (5/10=1/2), and B too 5/20 = 1/4 part of the whole work.

At this particular point in time the work left was 1 - (1/2 + 1/4) = 1/4 part only. B by his individual capacity this part was completed in 5 days, i.e.(1/4)/(1/20).

Now since B had completed the remaining in 5 days and A had worked for 5 days, the WHOLE WORK WAS COMPLETED 5+5=10 Days.

This is I hope the ANSWER you were looking for and I believe logically this is correct, because the whole work was to be completed on 7th day or Completed in 7 days, after 5 days it becomes crystal clear from the ratio of performance is exactly A : B = 1 : 2, that 1/4 part of the work for B would continue for 5 days.