WORK & TIME

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neya: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Jul 10, 2011 11:19 pm

by neya » Tue Sep 13, 2011 9:42 pm

20 men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?

a. 10 days
b. 20 days
c. 25days
d. 15 days

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Source: Beat The GMAT — Problem Solving | Tue Sep 13, 2011 9:42 pm

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue Sep 13, 2011 9:52 pm

20 men -> 30 days. 1 man 600 days and 15 men 40 days.
20 men can do 1/30 work in a day..
15 men can do 1/140 work in a day
a) 20 men work for 10 days: 1/3 work done. 15 men work for 25 days: 25/40 done. Nopes
b) 20 men work for 20 days: 2/3 work done. 15 men work for 15 days: 15/40 done. Nopes
c) 20 men work for 25 days: 5/6 work done. 15 men work for 10 days: 10/40 done. Nopes
d) 20 men work for 15 days: 1/2 work done. 15 men work for 20 days: 1/2 done. total = 1.
ImO D

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Tue Sep 13, 2011 10:31 pm

Let the work that needs to be completed be the typing of 60 pages

20 Men take 30 days to finish
So the rate for 20 men is 2 pages/day

If 20 mean take 30 days
Then 15 men would take 20*30/15=40 Days (# of men and days are inversely proportional)
So the rate of 15 men is 1.5 pages/day

Let the time worked by 20 men be x hrs
So in x hrs they will complete 2x of the work (work=rate*time)

Let the time worked by 15 mean be y hrs
So in y hrs they will complete 1.5y of the work (work=rate*time)

Now, total work done=60 i.e. 2x+1.5y=60 also x+y=35(as the total time taken by 20 men and 15 men is 35) Multiplying second equation by 2 we have 2x+2y=70 and then subtracting first equation from this we get y=20 and x=15. Which means that 20 workers have worked for 15 hours after which 5 workers left and the remaining 15 workers finished the job in the next 20 hrs. 15 hrs is the answer. Hence [spoiler]D[/spoiler]

I just prefer solving it algebraically!!

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tailoc: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Jun 15, 2011 11:38 am; Thanked: 1 times

by tailoc » Wed Sep 14, 2011 12:10 am

OA is D
Say that t is day when 5 workers leave
Say that number of units 20workers perform are 600 units.
=> rate = 600/30=20units/20workers=1unit/worker.
So,
Equation: q=r*t
20*1*t + 15*1*(35-t)=600
t=15 days

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 14, 2011 3:16 am

neya wrote:20 men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?

a. 10 days
b. 20 days
c. 25days
d. 15 days

Let rate per man = 1 unit per day.
Rate for 20 men = 20*1 = 20 units per day.
Work completed in 30 days = r*t = 20*30 = 600 units.
Rate after 5 men leave = 20-5 = 15 units per day.

From here, we can plug in the answers, which represent the number of days for which all 20 men should work.
We should start with one of the middle values (either 15 or 20).

Answer choice D: 15 days
Work completed by 20 men in 15 days = r*t = 20*15 = 300 units.
Remaining work = 600-300 = 300 units.
Time for remaining 15 men to produce 300 units = w/r = 300/15 = 20 days.
Total time = 15+20 = 35 days. Success!

The correct answer is D.

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by Scott@TargetTestPrep » Tue Dec 12, 2017 9:48 am

neya wrote:20 men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?

a. 10 days
b. 20 days
c. 25days
d. 15 days

We are given that 20 workers can complete a job in 30 days. Since rate = work/time, the rate of the 20 workers is 1/30. We can let x be the number of days it would take 5 fewer workers (i.e., 15 workers) to complete the job (from beginning to end); thus the rate of the 15 workers would be 1/x. Let's determine x using the following proportion:

20/(1/30) = (15)/(1/x)

600 = 15x

40 = x

Thus, the number of days it takes for the 15 workers to complete the job (from beginning to end) is 15 and their rate is 1/40.

However, we need to determine at what point in time 5 of the 20 workers should leave the job so that the work is completed in 35 days. We can let this be t, and note that the work done by the 20 workers in these t days plus the work done by the 15 workers after these t days (i.e., in 35 - t days) will be the complete job. Recall that work = rate x time, so we have:

(1/30)t + (1/40)(35 - t) = 1

t/30 + (35 - t)/40 = 1

Multiplying the equation by 120, we have:

4t + 3(35 - t) = 120

4t + 105 - 3t = 120

t + 105 = 120

t = 15

Answer: D

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Tue Dec 12, 2017 10:23 am

neya wrote:20 men can finish a piece of work in 30 days.When should 5 men leave the work so that it may be finished in 35 days?

a. 10 days
b. 20 days
c. 25days
d. 15 days

let one man can break one stone in a day
then 20 men in 30 days would break 20 x 30 = 600 stones
that is the complete work is to break 600 stones.

let us try each option and see with which option 600 stones can be broken

option A.... 20X10+15X25=200+375=575
.......B.....20X20+15X15=400+300=700
Clearly the option should be between A and C which is option D

Hence D is the correct option

we can varify also for option D

20X15+15X20=300+300=600

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