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If 20 diggers, each working at the same constant rate, can dig

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ritu1009
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If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   Updated on: 30 Aug 2023, 12:22
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If 20 diggers, each working at the same constant rate, can dig a 100-meter long trench in hard soil in 3 days, how many diggers are needed to dig a 180-meter long trench in soft soil in the same 3 days, given that a digger is 20% more productive in soft soil than in hard soil?

A. 25
B. 28
C. 29
D. 30
E. 32

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D

Originally posted by ritu1009 on 27 Dec 2018, 00:30.
Last edited by Bunuel on 30 Aug 2023, 12:22, edited 3 times in total.
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   27 Dec 2018, 01:19
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If 20 diggers, each working at the same constant rate, can dig a 100-meter long trench in hard soil in 3 days, how many diggers are needed to dig a 180-meter long trench in soft soil in the same 3 days, given that a digger is 20% more productive in soft soil than in hard soil?

A. 25
B. 28
C. 29
D. 30
E. 32


20 diggers can dig a 100-meter trench in hard soil in 3 days.

1 digger can dig a \(\frac{100}{20} = 5\)-meter long trench in hard soil in 3 days.

1 digger can dig \(5*1.2 = 6\) meters in soft soil in 3 days, due to the 20% increase in productivity.

Therefore, to dig a 180-meter trench in soft soil within 3 days, \(\frac{180}{6} = 30\) diggers are required.


Answer: D
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   28 Dec 2018, 23:48
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Mo2men wrote:
ritu1009 wrote:
Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A. 25
B. 28
C. 29
D. 30
E. 32



Dear GMATinsight

Can you help please with this question? I tried to use the same concept you did below but failed:

https://gmatclub.com/forum/a-company-s- ... ght%20fuel

Thanks in advance


Mo2men

Please find below my explanation in the similar way

CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)

i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

i.e. \(\frac{(20 * 3)}{100} = \frac{(M_2 *1.2 * 3)}{180}\)

i.e. \(M_2 = 20*(180/100)/1.2\)

i.e. \(M_2 = 30\)

I hope this helps!!!
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   27 Dec 2018, 00:40
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ritu1009 wrote:
Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A.25
B.28
c.29
D. 30
E. 32


20 diggers can dig a 100-meter long trench in hard soil in 3 days.
In 1 day, 1 digger can dig 100/20/3 = 5/3 meter

with increased efficiency, In 1 day, 1 digger can dig 5/3*1.2 = 2 meter

No. of diggers required to dig 180 meter in 3 days with increased efficiency = 180/3/2 = 30

Answer D
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   28 Dec 2018, 01:33
ritu1009 wrote:
Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A. 25
B. 28
C. 29
D. 30
E. 32



time for 1 digger to dig : 60 days
so rate would be 100/60 = 5/3

soft soil rate = 5/3 * 1.2 = 2 mtrs per day

in 3 days they can dig 2*3= 6 mtrs
so for 180 mtrs = 180/6= 30 diggers required IMO D
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   28 Dec 2018, 13:18
ritu1009 wrote:
Working at their normal constant rates, 20 diggers can dig a 100-meter long trench in hard soil in 3 days. A construction company ordered the diggers to dig a 180-meter long trench in soft soil. If diggers can work 20% faster in soft soil than in hard soil, how many diggers are required to complete this task in 3 days?

A. 25
B. 28
C. 29
D. 30
E. 32



Dear GMATinsight

Can you help please with this question? I tried to use the same concept you did below but failed:

https://gmatclub.com/forum/a-company-s- ... ght%20fuel

Thanks in advance
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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   01 Jan 2019, 21:04
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Solution


Given:
    • 20 diggers can dig a 100 m long trench, in hard soil, in 3 days
    • Now, they must dig a 180 m long trench in soft soil
    • They can work 20% faster in soft soil than in hard soil

To find:
    • The number of diggers required to complete the task in 3 days

Approach and Working:
In Hard Soil:
    • 20 diggers can dig \(\frac{100}{3}\) m in 1 day
    • 1 person can dig \(\frac{100}{(3 * 20)} = \frac{5}{3}\) m in 1 day

In Soft Soil:
    • 1 person can dig \((\frac{5}{3} * 1.2) = 2\) m in 1 day
    • Thus, 1 person can dig (2 * 3) m = 6 m in 3 days

Therefore, we need \(\frac{180}{6} = 30\) diggers to dig 180 m in 3 days

Hence, the correct answer is Option D

Answer: D

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Re: If 20 diggers, each working at the same constant rate, can dig [#permalink] New post   08 Mar 2024, 00:36
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