M11-19

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

Show Answer

Official Answer

D

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

Bunuel · Accepted Answer

Official Solution:

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

Show Answer

Official Answer

D

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

varshaaaaa · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Nipunh · Answer

I did it differently, here's how

20 diggers x 3 days = 60 diggers day (total work) =100 m 
n diggers x 3 days = 60 diggers day x 1.8 =180m (work increased to 1.8x of the original)
On solving, 
3n =60x1.8
n=20x1.8=36
now, we see that productivity has increased by 20% hence 36/1.2=30 days.
you could have also directly did it like:
1.2n diggers x 3 days = 60 diggers day x 1.8 (that productivity/efficiency has increased by 20%) and get 30 directly.

hope this helps.

Matteo13120 · Answer

Can we use the Proportion Method to solve this type of question?

I've tried this method provided by TTP but I didn't get the good answer. (see the screenshot below)

Bunuel · Answer

You can find several alternative methods here: https://gmatclub.com/forum/if-20-digger ... 85202.html Hope it helps.

adarsh2209 · Answer

I like the solution - it’s helpful.

M11-19

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