6. Two men can do a piece of work in 6 hours and 4 hours respectively.

1.	6. Two men can do a piece of work in 6 hours and 4 hours respectively. After the first has worked forhours, he is joined by the other. By when should the work be completed?
Answer» Let the first person be A and second person be B A can complete the work in 6 hoursi.e For one hour, A completes one-sixth of total work B can complete the work in 4 hoursi.e For one hour, B completes one-fourth of total work Together they do five-twelfth of total worki.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)

6. Two men can do a piece of work in 6 hours and 4 hours respectively. After the first has worked forhours, he is joined by the other. By when should the work be completed?

Answer»

Let the first person be A and second person be B

A can complete the work in 6 hoursi.e For one hour, A completes one-sixth of total work

B can complete the work in 4 hoursi.e For one hour, B completes one-fourth of total work

Together they do five-twelfth of total worki.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)