Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 20:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If x men can do a job in h days, how long would y men take to do the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56257
If x men can do a job in h days, how long would y men take to do the  [#permalink]

### Show Tags

26 Feb 2018, 23:25
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:04) correct 45% (01:10) wrong based on 66 sessions

### HideShow timer Statistics

If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
If x men can do a job in h days, how long would y men take to do the  [#permalink]

### Show Tags

26 Feb 2018, 23:48
2
Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

If x men do a job in h days, 1 man will do the work in $$hx$$ days*

Therefore, y men will have $$\frac{hx}{y}$$ days to do the same job (Option B)

*If x=5 men do a work in 20 days(assuming a man does 1 unit a day) they would a total of 100 units.
If 1 man must finish the work on his own(rate - 1 unit/day), he takes 100 days to finish the 100 units.
_________________
You've got what it takes, but it will take everything you've got
Senior SC Moderator
Joined: 22 May 2016
Posts: 3077
If x men can do a job in h days, how long would y men take to do the  [#permalink]

### Show Tags

27 Feb 2018, 19:30
Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

Algebra
The standard work formula is (R * T) = W

When problems include "number of workers" (or machines), you can modify the standard formula.

Then manipulate it just as you would RT=W, to find what you need.

Add one more variable to LHS, thus:
(# of men$$* R * T) = W$$

Values given:
# = $$x$$
T = $$h$$ (days)
W = 1 (job)

Find the rate of one man.
(# of men) * R * T = W

$$R = \frac{W}{(Number*T)}$$

$$Rate =\frac{1}{x*h}=\frac{1}{xh}$$

At that rate, how long will it take $$y$$ to do the same job?
# of men = $$y$$
Rate = $$\frac{1}{xh}$$
Time = ??
Work = 1 (job)

(# of men) * R * T = W
$$T=\frac{W}{(Number*Rate)}$$

$$T=\frac{1}{(y*\frac{1}{xh})}=\frac{1}{(\frac{y}{xh})}=1*\frac{xh}{y}=\frac{xh}{y}$$

Assign values
To avoid more than one correct answer:
-- don't use 1 in rate problems, and
-- include one slightly larger number

(# of men) * Rate * Time = Work
Let x (# of men) = 2
Let h (# of days) = 3
Let y (new # of men) = 8
Work = 1 job

Rate of one man?
(#) * R * T = W
(2) * (R) * (3) = 1
Rate = $$\frac{1}{(2*3)}$$
Rate of one man = $$\frac{1}{6}$$

At that rate, time it will take y=8 men to do the same job?
(Number of men) * R * T = W

T = $$\frac{W}{(Number*Rate)}$$

Time = $$\frac{1}{(8*\frac{1}{6})}=\frac{1}{(\frac{8}{6})}=1*\frac{6}{8}=\frac{3}{4}$$

With x=2, h=3, and y=8, find the answer that yields $$\frac{3}{4}$$ (days)

A. x/h: $$\frac{2}{3}$$. NO

B. xh/y: $$(\frac{2*3}{8})=\frac{6}{8}=\frac{3}{4}$$ MATCH

C. hy/x: $$(\frac{3*8}{2})=\frac{24}{2}=12$$. NO

D. xy/h: $$(\frac{2*8}{3})=\frac{16}{3}$$. NO

E. x/y: $$(\frac{2}{8})=\frac{1}{4}$$. NO

P.S. A modified RT=W chart, with (# of workers) added to LHS, usually makes these problems easier.
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
Manager
Joined: 23 Sep 2016
Posts: 237
Re: If x men can do a job in h days, how long would y men take to do the  [#permalink]

### Show Tags

27 Feb 2018, 23:06
Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

IMO B total work will be X*h and to find number of days we need to divide it by y
It will be easy to understand by plugging value in question:-
X=10 h=1 and y=3
total work is 10 and number of hours that 3 man will complete is 10/3= 3.33
if you will plot above assumed values in question only B will give u answer as 3.333
If you like my explanation then please prove me KUDOS
Re: If x men can do a job in h days, how long would y men take to do the   [#permalink] 27 Feb 2018, 23:06
Display posts from previous: Sort by