Question

If 12 Men or 15 Women can do a job in 20 days working 6 hours per day, how many men are required to work with 5 women to complete a work in 9 days working for 5 hours per day? (time and work 11)
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Answer 1

Answer:

A work done by 12 men or 15 women in 20 days. What is the time taken by 4 men and 5 women to complete this?

If twelve men can do it in twenty days that means each one can do it in 12/20 or 3/5 of a day. And the women can each do it in 3/4 of a day.

But the real problem comes when you try to get the men and women to work together. As you can see from the beginning of the problem they don't normally do that. So I think you would have to have them brought in separately. Unfortunately we really don't know whether the group that comes in to finish what the first group left will want to finish or just mess it up to get rid of the other crew.

Because of that I would say we should multiply 3/4x3/5 and then co

Let the efficiency of 1 man alone and 1 woman alone be x and y days respectively i.e. 1 man alone takes x days to finish the same work.

Then, 1 man alone would do 1/x of the work in a day, while 1 woman alone would do 1/y of the work in a day.

Work done by 1 man and 1 woman together in 1 day = 1/x + 1/y

Now, Work done = Efficiency of worker * Number of workers * Number of days.

Using this, we have an equation:

(12/x + 15/y) * 20 = 1

Dividing this by 3:

(4/x + 15/y) * 20 = 1/3

Taking the 3 to the other side:

(4/x + 5/y) * 60 = 1

Since 4/x + 5/y is the work done by 4 men and 5 women together in a day, they would take 60 days to complete the same amount of work.

Simpler method:

12 men and 15 women take 5 days to complete the work.

1/3 of the workers would take thrice the amount of time to do the same work.

They’d take 60 days to do it.

Answer 2

28 men are required to work with 5 women to complete a work in 9 days working for 5 hours per day

Given,

12 men work 20 days with 6 hours per day to complete the job

15 women work 20 days with 6 hours per day to complete the job

To Find,

No. of men required to work with 5 women to complete the job in 9 days working 5 hours per day

Solution,

We are given that 12 men work 20 days with 6 hours per day to complete the job

Also, we are given that 15 women work 20 days with 6 hours per day to complete the job

⇒ 12m(20×6) = 15w(20×6)

⇒ 12m= 15w

to find the least value that m and w can assume, 12m = 15w = LCM(12,15)

LCM(12,15) = 60

Therefore, m = 5 and w = 4

⇒ Work done = 12×5(20×6) = 7200 units

The work to be done is also equal to 7200 units

Let the no. of men required to complete the job be x.

Total efficiency = (xm + 5w)(9×5) = 7200

⇒ 45(5x + 5×4) =7200

⇒ 5x + 20 = 160

⇒ 5x = 140

⇒ x = 28

Therefore, the required no. of men = 28

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