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A certain number of men complete a piece of work in 60 days. If there

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rxs0005
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A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   07 Jan 2005, 16:11
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A certain number of men complete a piece of work in 60 days. If there were 8 men more the work would have been completed in 10 days less. How many men were there originally?

A. 10
B. 20
C. 30
D. 40
E. 50
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D
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banerjeea_98
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   07 Jan 2005, 17:58
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40.

If there are x workers in first case 1 man will take 60x. In second it will be 50(x+8)

60x = 50x + 400
x = 40
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   07 Jan 2005, 23:16
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suppose total number of men = x

x men can work a job in 60 days
x men can work 1/60 job in 1 day
1 man can work 1/60x in 1 day..........................1

x+8 can do the same job in 50 days
similarly,
1 man can do 1/50(x+8) job in 1 day ..............2

from 1 and 2, 1/60x = 1/50(x+8)

solving the equation, x = 40 men.
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   09 Jan 2005, 10:09
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40.
x-----60 days
x+8----50 days.
(x+8)50=60x
50x+400=60x
therefore, x=40.
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   05 Nov 2018, 04:50
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Applying MDH method
X*60=(x+8)*50

On solving; x=40

Posted from my mobile device
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A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   06 Nov 2018, 08:08
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rxs0005 wrote:
A certain number of men complete a piece of work in 60 days. If there were 8 men more the work would have been completed in 10 days less. How many men were there originally?

A. 10
B. 20
C. 30
D. 40
E. 50



we are asked to find out the no. of workers there were at the beginning .

Let the no. of worker be x. Now we can calculate the total work algebraically.

60*x = total work.

but if there were 8 more men this task could be performed 10 days early. It means we could do the task in 50 days.

(x + 8) = total no. of men

So, 50(x + 8) = total work.

60x = 50(x + 8)

x = 40.

the best answer is D.

Useful property:

no. of men * rate * time = work.
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   06 Nov 2018, 08:38
rxs0005 wrote:
A certain number of men complete a piece of work in 60 days. If there were 8 men more the work would have been completed in 10 days less. How many men were there originally?

A. 10
B. 20
C. 30
D. 40
E. 50



let x be inital # of men

x = 60
x+8= 50
cross multiply

50x = 60(x+8)

50x=60x+480

50x-60x = 480

-10x = 480

x = - 48

strange why negative num i got :? does it mean that there was only 1 men who was working for 40 men :lol:

anyway 40-8 = 40 :)
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   07 Nov 2018, 19:08
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rxs0005 wrote:
A certain number of men complete a piece of work in 60 days. If there were 8 men more the work would have been completed in 10 days less. How many men were there originally?

A. 10
B. 20
C. 30
D. 40
E. 50


The rate for the unknown number of men is 1/60.

The rate for 8 more men is 1/50.

We can let n = the original number of men and create the proportion:

n/(1/60) = (n + 8)/(1/50)

60n = 50n + 400

10n = 400

n = 40

Answer: D
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   17 Sep 2022, 01:09
We know that
A = RT
Where, A=amount of work
R=rate of work
T=Time taken to complete work

Here, Amount of work =1
And R=1/60 (for first case)
So x man would complete it in 1/60x rate.
Forsecondcase R= 1/50(8+x)

Now both rates shall be equal,so

60x = 50(8+x)
Hence x=40

Posted from my mobile device
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink] New post   18 Apr 2024, 16:19
PulakNasim wrote:
Applying MDH method
X*60=(x+8)*50

On solving; x=40

Posted from my mobile device

­Can you explain MDH methods for this one please
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Re: A certain number of men complete a piece of work in 60 days. If there [#permalink]
18 Apr 2024, 16:19
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