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64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days
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Bunuel
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64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days [#permalink] New post  21 Jan 2021, 04:00
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64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75 m long, 4 m wide and 3 m deep?

(A) 18
(B) 27
(C) 36
(D) 45
(E) 47
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meanup
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Re: 64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days [#permalink] New post  24 Jan 2021, 18:45
\(\frac{64*5*12}{50*2*2}=\frac{8*80*x}{75*4*3}\)

\(x=27\)
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chetan2u
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Re: 64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days [#permalink] New post  24 Jan 2021, 19:21
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Bunuel wrote:
64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75 m long, 4 m wide and 3 m deep?

(A) 18
(B) 27
(C) 36
(D) 45
(E) 47


64 person can dig 50*2*2 or 200m^3 in 5 days working 12 hrs daily.
So, 1 person can dig 1m^3 in \(\frac{5*64*12}{200}\) working 1 hr daily.
Therefore, 80 person can dig 75*4*3 or 900m^3 in \(\frac{5*64*12}{200}*\frac{900}{80*8}=\frac{5*12*9}{2*10}=27\)

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