Question

Two man 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 other. By when should work be completed.

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

Answer 2

Let the two men be A & B

Given:

A can do a piece of work in 6 hours & B can do in 4 hours.

A’s 1 hour work = 1/6


B’s 1 hour work = ¼


Both (A+B)’s 1 hour work = 1/6 + 1/4 = 5/12

=( 2+3)/12= 5/12

Both (A+B)’s 1 hour work = 5/12

After the first has worked for 2 hours ' he is joined by the other,

(A)’s 2 hour work = 2(1/6) = 2/6= ⅓

Remaining work = 1-1/3 = (3-1)/3= ⅔


5/12 work is done by (A+B) in 1 hrs


2/3 work is done by (A+B) in 12/5 × 2/3 = 8/5 hrs

Total time taken to be completed the work = 2 + 8/5 = 18/5 = (10+8)/5= 18/5
= 3 ⅗ hrs = 3hr 36 min

Hence, the Total time taken to be completed the work = 3 3/5=3 hrs 36 min.

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Hope this will help you....