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A team of eight men is digging ditches and each man is working at the

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Bunuel
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A team of eight men is digging ditches and each man is working at the [#permalink] New post   17 Apr 2017, 01:08
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A team of eight men is digging ditches and each man is working at the same constant rate. If after digging the first 4 ditches in 6 hours, the team loses two of the men to injury, how many hours will it take the remaining men to dig the next two ditches?

A. 2
B. 4
C. 6
D. 8
E. 12
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Re: A team of eight men is digging ditches and each man is working at the [#permalink] New post   17 Apr 2017, 02:30
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8*6 ManHours = 4 ditches -->

2 ditches = 24 Manhours

Time required for 6 men = 24/6 = 4 hours

Answer: B
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A team of eight men is digging ditches and each man is working at the [#permalink] New post   Updated on: 27 Apr 2017, 04:13
Assume there are 72 units of work to be done.
Let the rate of work be x
It takes 8 men to build the first 4 ditches(66.67% of the total work), 6 hours
8*6*x = 48 units(since 2/3rds of the work is completed)
Every man does 1 unit of work in an hour.
2 men are injured, Total men working now are 6.
We need to complete 24 units of work with 6 men.
Total hours taken to complete the work from here on is 6 hours(24units / 6men*1 unit/hour)
(Option B)

Originally posted by pushpitkc on 27 Apr 2017, 03:17.
Last edited by pushpitkc on 27 Apr 2017, 04:13, edited 2 times in total.
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Re: A team of eight men is digging ditches and each man is working at the [#permalink] New post   27 Apr 2017, 04:04
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Given: 8 men ---dig---> 4 ditches ---in---> 6hrs
That implies 1 man ---digs---> 4 ditches ---in---> 6*8=48hrs
To find: 2 ditches take how many hours and how many men?
How many hrs?
We know 1 man ---digs---> 4 ditches ---in---> 48hrs
That implies 1 man ---digs---> 2 ditches ---in---> 24hrs @1st variable
How many men?
We know that out of 8, 2 men are injured = 8-2= 6 men left @2nd variable
Now from @1 and @2 variables we can deduce the required answer
i.e.,
1 man ---digs---> 2 ditches ---in---> 24hrs
Implies 6 men ---dig---> 2 ditches ---in---> 24/6 = 4 hrs (option B)
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A team of eight men is digging ditches and each man is working at the [#permalink] New post   27 Apr 2017, 10:46
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Ans is B: 4 hrs

Follow the old school formula for this:
(Man*Day*Hrs)/Work

Let z be the no.of hrs required by 6 men to dig 2 ditches.

so,
8*6/4 = 6*z/2

This gives z=4

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Re: A team of eight men is digging ditches and each man is working at the [#permalink] New post   02 May 2017, 16:45
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Bunuel wrote:
A team of eight men is digging ditches and each man is working at the same constant rate. If after digging the first 4 ditches in 6 hours, the team loses two of the men to injury, how many hours will it take the remaining men to dig the next two ditches?

A. 2
B. 4
C. 6
D. 8
E. 12



We are given that a team of 8 men can dig 4 ditches in 6 hours, and each man is working at the same constant rate. Thus, the rate of these 8 men is 4/6 = ⅔ and the rate of 1 man is (⅔)/8 = 1/12.

We are also given that the team loses 2 men due to injury; thus, the rate of the remaining 6 men is 6 x 1/12 = ½. Since time = work/rate, the time needed for the remaining 6 men to dig 2 ditches is 2/(½) = 4 hours.

Answer: B
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A team of eight men is digging ditches and each man is working at the [#permalink] New post   02 May 2017, 20:28
Bunuel wrote:
A team of eight men is digging ditches and each man is working at the same constant rate. If after digging the first 4 ditches in 6 hours, the team loses two of the men to injury, how many hours will it take the remaining men to dig the next two ditches?

A. 2
B. 4
C. 6
D. 8
E. 12


rate of 1 man=4/(8*6)=1/12 ditch per hour
let h=hours needed for 6 men to dig 2 ditches
6*h*1/12=2
h=4 hours
B
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Re: A team of eight men is digging ditches and each man is working at the [#permalink] New post   04 Jun 2017, 11:31
8 men --- 4 ditches --- 6 Hrs
8 men --- 2 ditches --- 3 Hrs
1 man --- 2 ditches --- 8*3 = 24 Hrs

So 6 men dig 2 ditches in 24/6 = 4 Hrs
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Re: A team of eight men is digging ditches and each man is working at the [#permalink] New post   27 Jul 2020, 22:00
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Re: A team of eight men is digging ditches and each man is working at the [#permalink]
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