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8 men can dig a pit in 20 days. If a man works half as much again as

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Bunuel
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8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  27 Apr 2021, 06:00
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8 men can dig a pit in 20 days. If a man works half as much as a boy, then 4 men and 9 boys can dig a similar pit in:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 18 days
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GMATinsight
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  27 Apr 2021, 06:09
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Bunuel wrote:
8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 18 days


CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)


1 men = 1.5 boy
8 men = 8*1.5 = 12 boys
i.e. 4 men and 9 boys = 4*1.5+9 = 15 boys

i.e. \(\frac{(12 * 20)}{1} = \frac{(15 * T_2)}{1}\)

ie.. \(T_2 = \frac{12*20}{15} ≈ 16\) days

Answer: Option D

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Nidzo
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  27 Apr 2021, 06:41
Let men be m and boys be b

8/m = 1/20 therefore m = 160 (ie 1 man will dig the same hole in 160 days)

as m = 1.5b
it will take 1 boy 240 days to dig the same hole.

Question asks for how long it will take 4 men and 9 boys to dig a hole, which is the same as asking how long will it take 15 boys (given that 4m = 6b) to dig the same hole.

15/240 = 1/n
15n = 240
n = 16

Answer D.
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ManyataM
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  27 Apr 2021, 08:16
Bunuel wrote:
8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 18 days


In the question it says that a man works half as much again as a boy. what does this mean? I am trying to multiply the rate by 2 as it says man has 1/2 efficiency of boy. Can you explain?
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VelvetThunder
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  11 Jul 2022, 23:15
ManyataM wrote:
Bunuel wrote:
8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 18 days


In the question it says that a man works half as much again as a boy. what does this mean? I am trying to multiply the rate by 2 as it says man has 1/2 efficiency of boy. Can you explain?

Kind of poorly constructed question - If a man works half as much again as a boy implies 1.5X not 0.5X
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GmatPoint
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  12 Jul 2022, 01:39
Let the total work be 480 units(8*20*1.5 units).

Since 8 men work 480 units in 20 days, 1 man will work 480/8*20 units = 3 units

Also, as a man works 1.5 times as a boy, 1 boy will work 3/1.5 units per day.

Thus, a boy will work 2 units per day.

Work done by 4 men and 9 boys in 1 day = 3*4 + 2*9 = 30 units.

Total time taken by 4 men and 9 boys will be 480/30 days = 16 days.

Thus, the correct option is D.
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Vadera96
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink] New post  13 Jul 2022, 08:55
Bunuel wrote:
8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days
(E) 18 days


Can we normalize fixing errors in the questions?...
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Re: 8 men can dig a pit in 20 days. If a man works half as much again as [#permalink]
13 Jul 2022, 08:55
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