Question

one men can do a piece of work in 3hours ; another can do the work in 2 hours .how long will they take if they work together​

Answer 1

Let the men be A and B can complete the piece of work in x hours

ATQ

A completes the work in 3 hours

A does (1/3) part of work in 1 hour

similarly

B completes the work in 2 hours

B does (1/2) part of work in 1 hour

So, if they work together, the portion of work they will complete in 1 hour =

(1/3) + (1/2) = 5/6

So the time taken to complete the work by A and B together is (6/5) hours = 1 hour and 12 minutes.

So 1 hour 12 minutes is required answer.

Answer 2

Answer :-

It takes 1 hour 12.minutes if they both are worked together.

Explanation :-

Given

One man can do a piece of work in 3 hours

So, One man's 1 hour work = 1/3

Another man can do a piece of work in 2 hours

So, another man's 1 hour work = 1/2

We know that

Two men's 1 hour work = One man's 1 hour work + Another man's 1 hour work

= (1/3) + (1/2)

Taking LCM

= (2 + 3)/6

= 5/6

Two men's 1 hour work = 5/6

⇒ Two men together can complete the work in 6/5 hours = 1 1/5 hours = 1 hour 12 minutes

[ ∵ (1/5) th hour = (1/5) * 60 minutes = 12 minutes]

∴ It takes 1 hour 12.minutes if they both are worked together.

Remember :-

Total work done in = 'N' hours

⇒ Work done in 1 hour = (1/N)th amount of work

Also

Work done in 1 hour = (1/N)th amount of work

⇒ Total work done in = 'N' hours