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# M20-03

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Math Expert
Joined: 02 Sep 2009
Posts: 46280

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16 Sep 2014, 01:07
00:00

Difficulty:

5% (low)

Question Stats:

79% (00:55) correct 21% (00:53) wrong based on 163 sessions

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If 2 excavators can dig a 10-meter long trench in 50 minutes, how long will it take 3 excavators to dig a 15-meter long trench? (Assume the excavators are working at the same constant rates)

A. 45 minutes
B. 50 minutes
C. 52 minutes
D. 54 minutes
E. 60 minutes

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Math Expert
Joined: 02 Sep 2009
Posts: 46280

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16 Sep 2014, 01:07
1
Official Solution:

If 2 excavators can dig a 10-meter long trench in 50 minutes, how long will it take 3 excavators to dig a 15-meter long trench? (Assume the excavators are working at the same constant rates)

A. 45 minutes
B. 50 minutes
C. 52 minutes
D. 54 minutes
E. 60 minutes

1 excavator can dig a 10-meter long trench in $$50*2=100$$ minutes. So, it can dig a 15-meter long trench in $$100*1.5=150$$ minutes.

Hence, 3 excavators can dig a 15-meter long trench in $$\frac{150}{3}=50$$ minutes.

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Senior Manager
Joined: 11 Nov 2014
Posts: 344
Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)

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02 Sep 2016, 23:06
10 meters 50 mins
so x meters 1 min
1/5 meters 1 min

so 3/5meters by 3 machines in 1 min
so for 15 meters =
3x/5=15
x = 25 minutes

Where am I going wrong?
Intern
Joined: 21 Dec 2015
Posts: 25
WE: Account Management (Commercial Banking)

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07 Dec 2016, 08:14
1
1
paidlukkha

10 meters 50 mins
so x meters 1 min
1/5 meters 1 min

so 3/5meters by 3 machines in 1 min
so for 15 meters =
3x/5=15

Two mistakes have been made.

1/5 metres per minute is the work done by 2 machines.
hence 1/10 work is done in 1 minute by 1 machine (1/5 / 2).

Now, 1/10 * 3 = 3/10 work done by 3 machines in 1 minute.

Second mistake is : 3x/5=15 (where you've equated work to work)

Back to what i said, 3/10 is work done by 3 machines in 1 minute.
Hence, work to be done is 15 metres. So, 15 / 3/10 = 50 minutes.

Hope this helps.
Intern
Status: Don't watch the clock,Do what it does, Keep Going.
Joined: 10 Jan 2017
Posts: 45

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16 Sep 2017, 08:22
let x be the rate of work . Now,
total work/(number of days * time*rate of work) is the basic formula;

As per question
let t be the time
10/(2*50*x)=15/(3*t*x)
solving t=50
hence answer is B
Re: M20-03   [#permalink] 16 Sep 2017, 08:22
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# M20-03

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