Question

2 men can do a peice of work in 6 hours and 4 hours respectively. After the first has worked for 2 hours' he is joined by the other. By when should the work be compleated?

Answer 1

Let the first person be A and second
person be B
A can complete the work in 6 hours
i.e For one hour, A completes one-sixth
of total work
B can complete the work in 4 hours
i.e For one hour, B completes one-
fourth of total work
Together they do five-twelfth of total
work
i.e (1/6)+(1/4) = (4+6)/24 = 10/24 =
5/12
Case 1:
As A worked for two hours, he would
complete one-third of the work.
The remaining work would be the two-
third part
5/12 is the part of work which is
completed together in an hour.
Divide 2/3 with 5/12
=> (2/3)/(5/12) = (2/3)*(12/5) = 24/15
= 8/5
So, the remaining part of the work is
completed in 8/5 hours (1 hr 36 min)
The total work is completed in 18/5
hours (3 hrs 36 min)
Case 2
As B worked for two hours, he would
complete half of the work.
The remaining work would be the half
part
5/12 is the part of work which is
completed together in an hour.
Divide 1/2 with 5/12
=> (1/2)/(5/12) = (1/2)*(12/5) = 12/10
= 6/5
So, the remaining part of the work is
completed in 6/5 hours (1 hr 12 min)
The total work is completed in 16/5
hours (3 hrs 12 min)
Note: I had given two cases because the
problem has not specified who is the
first person.
Hope it helps