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M20-03

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M20-03 [#permalink]

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New post 16 Sep 2014, 01:07
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Question Stats:

80% (00:52) correct 20% (00:43) wrong based on 143 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
[Reveal] Spoiler: OA

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Re M20-03 [#permalink]

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New post 16 Sep 2014, 01:07
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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.


Answer: B
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M20-03 [#permalink]

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New post 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?

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Re: M20-03 [#permalink]

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New post 07 Dec 2016, 08:14
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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.

Kudos [?]: 3 [1], given: 29

Intern
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Status: Don't watch the clock,Do what it does, Keep Going.
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Re: M20-03 [#permalink]

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New post 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

Kudos [?]: 17 [0], given: 45

Re: M20-03   [#permalink] 16 Sep 2017, 08:22
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