Work and men

[jyoticlub]

21 men were employed to do a work in a cetain time.When 1/3rd of the time was completed only a quarter of work was done.How many more men should be employed to complete the work in 3/4th of the scheduled time.

 

I got the answer as 11.(i am not sure)Can u help!!

 

Jyoti

[5614]

You can tell that is wrong just by looking at. They have done 25% of the work in 33% of the time, clearly they need more people. And 11 is less.

 

I wouldn't say I know how to do it because I don't, but here is my method of thinking:

 

Say it takes 3hrs to do all of the work (just because we are dealing with 3rds) so when 1/3 of the time is gone that is 1hr of work for each of the 21 men. If 21 people do 1 hour of work we have 21hours of work in total.

 

If 21hrs of work = 25% then 75% = 21*3 = 63 hours of work.

 

If we have 2/3 of the time then we have 2 hours. And we need 63hrs of work done in 2. So we need 63/2 men, which is 31.5 men, which we must round to 32 men.

 

Let's try putting that more mathematically:

 

Assume total working time for all men is 3 hours.

So 1/3 time = 1 hour

[math]21men \times 1hr = \frac{1}{4} work = 21[/math]

So 2/3 of the time is 2 hours

[math]Number Of Men \times 2hrs = \frac{3}{4} work = \frac{1}{4} work \times 3 = 21 \times 3 = 63[/math]

[math]No. Men \times 2hrs = 63[/math]

[math]No. Men = \frac{63}{2hrs} = 31.5 \to 32[/math]

[Dave]

Well, you just confirmed his answer; the question states "how many more men", not "how many men" Your answer of 32 corroborates his of an 11-man increase.

[5614]

Ah, yeah, good point... wrote down the data on some paper and worked it out, then forgot to actually read the question ... yeah, 11 more sounds good. Ah well, it was a nice question to do.

[abskebabs]

Eek! I got a different answer to you guys when doing this(you may notice I'm a complete amateur with latex, this took me way too long). I first worked out a rate the men would be working at by dividing the work done by the time. Then I divided this by the number of ppl to give me the rate per person. I thne worked out the rate that would be required to finish the work with a quarter of the time to spare. I had to first find the remaining time by taking away a third from 3 quarters. Finally I divided the required rate by the rate per person to give me a number.

[math]rate= \frac{\frac{1w}4}{\frac{t}3}= \frac{3w}{4t}[/math]

[math]rate/person= \frac{\frac{3w}4t}{21p}= \frac{w}{28tp}[/math]

[math]time.remaining=\frac{3t}{4}-\frac{t}{3}= \frac{5t}{12}[/math]

[math]requiredrate=\frac{\frac{3w}4}{5t/12}= \frac{9w}{5t}[/math]

Therefore to find the number of ppl needed after a third of the time has passed:

[math]No.people=\frac{9w/5t}{w/28tp}= \frac{252p}{5}= 50.4[/math]

Therefore the total number of ppl required to do the job in time after a third of the time has passed within 3 quarters of the time has to be at least 51.

You would therefore need 30 more ppl. I'm not sure if this is correct...

[5614]

I can't find a specific mistake in your calculations. I don't know if you can just use w, p & t as variables like that.

 

All I can really say is that you are using the wrong method and the wrong way of thinking about/approaching the problem. You've got the correct way (incl. solution) above so use that.

 

Sorry I can't help more.

[abskebabs]

I think I see the difference in our methods. I assumed that the work had to be done within 3 quarters of the total time after a third of the time had passed. It doesn't seem to me you took into account that the work needed to be completed within 3 quarters of the time, I think. I'm not sure:confused: ? Where's a maths moderator when you need one:rolleyes: .

[Dak]

none of your fancy squiggles and symbols for me... it's brute-forsing with basic maths all the way

 

21 people = 25% of total work (in 33% of total time)

 

{divide by 21}

 

1 person = 1.19% of total work (in 33% of total time)

 

or

 

(1 person) 1.19% of total work = 33% of total time

 

{divvy by 33}

 

(1 person) = 0.036% of total work = 1% of total time.

 

Now, they've used 33% of the time and need to complete the work 25% ahead of scedule, so they have 100% - 33% - 25% = 42% of the total time left.

 

{times by 42%}

 

(1 person) 1.51% of total work = 42% of total time

 

{or}

 

1 person = 1.51% of total work (in 42% of total time)

 

Now, they have 75% of the work outstanding, so times by 75/1.51 rounded up

 

{times 50}

 

50 people = 75.5% of total work (in 42% of total time).

 

which is enough to get the remaining work done in the time remaining.

 

and as they have 21 people, they need 50 - 21 = 29 more people.

 

Which, give-or-take for my rounding, is abskebabs' answre.

 

in summary: abskebabs was right, 5614 needs to read questions more carefully , and i still don't think all those funny squggles that you guys use are neccesary