Q25: If 42 men can do a work in 15 days, how many men are required to

complete it in 21 days?

A. 24

B. 36

C. 30

D. None of these

how?

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- Feb 10th 2011, 10:48 PMbahadarali42 men can do a work in 15 days, how many men for 21 days?
Q25: If 42 men can do a work in 15 days, how many men are required to

complete it in 21 days?

A. 24

B. 36

C. 30

D. None of these

how? - Feb 10th 2011, 11:13 PMpickslides
Was option A. your pick, or the actual answer?

I would try to solve $\displaystyle \displaystyle \frac{42}{15} = \frac{x}{21}$ - Feb 10th 2011, 11:30 PMguildmage
Then $\displaystyle x = 58.8$?

I'm not very good at this either. (Giggle)

But in my analysis, in 1 day, $\displaystyle \frac{1}{15}$ of the job is done by 42 men. This means that 1 man does $\displaystyle \frac{1}{630}$ of the job in one day.

In 21 days, a man does $\displaystyle \frac{21}{630}$ of the job. From here, it should be easy to know how many men are needed to get the job done in 21 days.

So I don't think (a) is the correct answer here. - Feb 10th 2011, 11:36 PMpickslides
Well it really depends on if there is any scaling involved in this problem. For example the more workers you have, the less number of days a job should take relatively.

This could be determined if an additional ratio/information was given.

But as this was posted in the pre-uni/pre-algebra thread I thought some simple ratios will do the job. My pick is option D. - Feb 10th 2011, 11:45 PMearboth
- Feb 11th 2011, 02:07 AMArchie Meade
- Feb 11th 2011, 06:19 AMSoroban
Hello, bahadarali!

Quote:

Q25: If 42 men can do a work in 15 days,

how many men are required to do it in 21 days?

. . (A) 24 . . (B) 36 . . (C) 30 . . (D) None of these

In 15 days, 42 men can do the job.

In one day, 42 men can do $\displaystyle \frac{1}{15}$ of the job.

In one day, one man can do $\displaystyle (\frac{1}{42})(\frac{1}{15}) = \frac{1}{630}$ of the job.

In 21 days, 1 man can do $\displaystyle (21)(\frac{1}{630}) = \frac{1}{30}$ of the job.

Therefore, it takes 30 men to do the job in 21 days.

- Feb 11th 2011, 07:18 AMHallsofIvy
Yet another way of thinking about it: 21 days is $\displaystyle \frac{21}{16}= \frac{7}{5}$ of the 15 days required by 42 men. Since

**more**men would take**less**time and vice-versa, this is an "inverse" proportion- invert the fraction. 21 days will require $\displaystyle \frac{5}{7}(42)= 5(6)= 30$ men.

(Pickslides was treating it as a**direct**proportion.) - Feb 11th 2011, 08:59 AMArchie Meade
Here's another "sideways glance" on this.

Suppose there was only 1 guy.

We'd need 42 of him to get the job done in 15 days.

So, in 15 days he'd have had to do 42 times as much work as he ordinarily can do.

Therefore, he needs 42 days to do what 42 guys do in 1 day.

So he needs 42(15) days to do what 42 guys do in 15 days.

That's 630 days.

In 21 days, he'd need to do the work of 30 guys each day.

Or, it takes 42(15)=630 man-days to complete the work.

In 21 days, 30 men are required.