Question

Two men can do a piece 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 completed ​

Answer 1

Answer:

your answer is A and B together do (1/6)+(1/4) = (2/12)+(3/12) = 5/12th part of the work in an hour. To complete the remaining 2/3rd of the work A and B will need to work for (2/3)/(5/12) or 2*12/(3*5) or 8/5 hours or 1.6 hours.

Answer 2

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