X number of men can finish a piece of work in 30 days

Question

X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
(A) 10 
(B) 11
(C) 12 
(D) 14
(E) 15

ganand · Accepted Answer

Hi,

X number of men can finish a piece of work in 30 days. ==> Total work = 30X Men days. -- (1)

If there were 6 men more, the work could be finished in 10 days less. ==> Total work = (X+6)*20 days -- (2)

By (1) and (2) we have:

30X = (X+6)*20 => 10X = 120 => X = 12 men.

Thanks.

KarishmaB · Answer

Using Ratios:

X men do 1/30th of the work per day.

X+6 men will do 1/20th of the work per day.

So ratio of men in the two cases is (1/30)/(1/20) = 2/3

On the ratio scale, the additional 1 is actually 6 so the multiplier is 6. Hence original number of men = 2*6 = 12

Answer (C)

Ratios Concept Video:  https://youtu.be/5ODENGG5dvc 
Ratios Post:  https://anaprep.com/arithmetic-ratios-the-one-where-it-all-starts/

vitaliyGMAT · Answer

y-#of days one man will finish the work.

\frac{x}{y} = \frac{1}{30}

y = 30x

\frac{x + 6}{y} = \frac{1}{20}

\frac{x + 6}{30x} = \frac{1}{20}

20x + 120 = 30x

x = 12

Answer C

gracie · Answer

rate of 1 man per day=1/30x
(x+6)*1/30x*20=1
x=12
C

okfan01 · Answer

Hi Karishma, can you break this down a bit more? I understand the ratio of rates is 2/3, but what did you mean "on the ratio scale, the additional 1 is actually 6"?

KarishmaB · Answer

You have the ratio scale, a multiplier and the actual values.

e.g. On the ratio scale, A:B = 2:3.
If the multiplier is 6, actual values are A = 6*2 = 12 and B = 6*3 = 18

ScottTargetTestPrep · Answer

We are given that X men can complete a job in 30 days. Since rate = work/time, the rate of the X men is 1/30. We are also given that if 6 more men were added, the work could be finished in 10 fewer days (i.e., the work could be finished in 20 days). Thus the rate of X + 6 men would be 1/20. To determine X, we create the following proportion:

X/(1/30) = (X + 6)/(1/20)

30X = 20(X + 6)

30X = 20X + 120

10X = 120

X = 12

Answer: C

okfan01 · Answer

Thanks! This was a good read.

keats · Answer

You can straight away apply a formula here.

(M1D1H1)/W1 = (M2D2H2)/W2

Where M1, M2 = Number of men/women
H1,H2 = Number of hours worked
D1,D2 = Number of days worked
and 
W1,W2 = Work done

Here, the case will be

(X)30 = (X+6)(20)
X=12

EMPOWERgmatRichC · Answer

Hi saswata4s,

This question can be solved by TESTing THE ANSWERS. Since the numbers involved in the prompt are all EVEN numbers (and there are no fractions or decimals involved), then it's likely that the correct answer will also be an even number. This is essentially a rate question, so it will help to think in those terms...

Let's TEST Answer A: 10 workers

IF... 10 workers require 30 days to complete a job, then that is (10)(30) = 300 worker-days of effort to complete the task.
With 10+6 = 16 workers, we would need 300/16 = 18 3/4 days to complete the task. This difference does NOT match what we were told (it's supposed to be 20 days). Eliminate Answer A.

Let's TEST Answer C: 12 workers

IF... 12 workers require 30 days to complete a job, then that is (12)(30) = 360 worker-days of effort to complete the task.
With 12+6 = 18 workers, we would need 360/18 = 20 days to complete the task. This is an exact match for what we were told, so this MUST be the answer.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

ganand · Answer

Hi EMPOWERgmatRichC,

I think if options are in increasing/decreasing order then we should start checking with middle option, i.e. (C). It helps us to eliminate two other options in one shot.

Thanks.

EMPOWERgmatRichC · Answer

Hi ganand,

When TESTing THE ANSWERS, it helps to consider all of the information that you're given (including the 'design' of the answer choices and the specific question that is asked) when choosing which answer to TEST first. To that end, starting with Answer C is often not the best option (as 80% of the time you'll be forced to check a second option to get to the correct answer).

GMAT assassins aren't born, they're made,
Rich

trungn2015 · Answer

(1): X*(1/m) = 1/30 (X men do 1/30 work a day)
(2): (X+6)*(1/m) = 1/20 ((X + 6) men do 1/20 work a day)
(1)/(2) = X/(X+6) = 2/3 --> 3X = 2X + 12 --> X = 12

jxav · Answer

1/20-1/30=1/60
So 6 men will make 1/60 more job per day which makes 1 men do 1/360 job per day
360/30= 12 men as original number

muthappashivani · Answer

What if you consider the total units to be 600 and so with
X men -30 days - 600 units then in 1 day he makes 20 units.
therefore for X men it is 20X units / day
X+6 men - 20 days - 600 units then in 1 day he makes 30 units
therefore for X+6 men it is 30 (X+6)=30X+180. Then equate the two to get the value of X. But i am unable to get the answer.
Can someone please let me know why is my method wrong and where am i getting deviated. Thank you :oops:

ganand · Answer

Hi  muthappashivani ,

Please refer the highlighted part.

x men 30 days - 600 units => x men in 1 day - 20 units => 1 men in 1 day - 20/x units. --- (1)

x+6 men 20 days - 600 units => x+6 men in 1 day - 30 units => 1 men in 1 day - 30/(x+6) units. ---(2)

Equate (1) and (2), we have:

\frac{20}{x} = \frac{30}{x+6} \Rightarrow 30x = 20x + 120 \Rightarrow x = 12

Hope it helps.

Thanks.

CrackverbalGMAT · Answer

M1 D1 = M2 D2 where M and D stand for number of men and days respectively.

=> x * 30 = (x+6) * 20

=>x* 30 = 20x + 20*6

=>10x = 120

=> x = 120 /10 =12

(option c)

D.S
GMAT SME

IsilAymanStan · Answer

Can you please clarify a few things for me?

What exactly do you mean by "the additional 1 is actually 6"? What is the "additional 1"? And, is 6 obtained from the question stating "If there were 6 men more"?

KarishmaB · Answer

This is the conversion from ratios to actual values. The ratio of men in the two cases is 2 : 3 a difference of 1 between them. But actual difference between them is 6 people. This means we have 12 and 18 men respectively in the two cases.

I have discussed the ratios method in detail here:

Ratios Concept Video:  https://youtu.be/5ODENGG5dvc 
Ratios Post:  https://anaprep.com/arithmetic-ratios-the-one-where-it-all-starts/

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