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

Question

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

Bunuel · Accepted Answer

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

GMATinsight · Answer

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!!!

shashankism · Answer

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

Archit3110 · Answer

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

Mo2men · Answer

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

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

Adarsh_24 · Answer

Alternate method:

20D * 3days => 100m
X 6D/5 * 3 days => 180m( soft soil digger rate is 6/5 of hard soil digger)

100 * (6x/5)/20 * 3/3 = 180
100 * 6x/100 = 180
X=30

Ters · Answer

Work (w) = rate (r) * time (t)

let x be number of diggers:
    
 W 
 r 
 t 
 
  20x 
 100 
 100/3 
 3 
 
  x 
 100 
 100/60 
 60 
 
  30x 
 180 
 180/30 
 30

\frac{100}{60}x * \frac{6}{5} = \frac{180}{3} 
 x=\frac{180}{6} 
 x=30

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

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

Prep Toolkit

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