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# 20 workmen can make 35 widgets in 5 days. How many workmen are needed

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Math Expert
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20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 00:58
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20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60
[Reveal] Spoiler: OA

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Manager
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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 01:15
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35w--------5days------20Men
1w----------5days------20/35Men
1w----------1day---------(20/35)*5 Men
105w-------1day--------(20/35)*5*105Men
105w-------5days-------(20/35)*5*105*1/5 Men
Ans=60 Men

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 04:15
1
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Expert's post
Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

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. $$\frac{(20 * 5)}{35} = \frac{(M_2 * 5)}{105}$$

i.e. $$M_2 = 60$$

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 05:28
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Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

$$20$$ workmen can make $$35$$ widgets in $$5$$ days.

Let the number of workmen to make $$105$$ widgets in $$5$$ days be $$= x$$

Number of days ie; $$5$$ is same in both cases, hence we can ignore that.

$$\frac{20}{35} = \frac{x}{105}$$

$$x = \frac{20*105}{35} = 60$$

Hence $$60$$ men are required to make $$105$$ widgets in $$5$$ days.

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20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 06:27
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Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

W = # * r * t, where # = number of workers. Manipulate that equation in same way as W = rt.

Individual worker's rate is 35/(5*20), or 35/100, or $$\frac{7}{20}$$

New # of workers, using individual rate, is 105/[(7/20)*5], or 105/(35/20), or 105/(7/4) =

105 * $$\frac{4}{7}$$ = 60

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20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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07 Jul 2017, 10:17
Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

let w=workmen needed
because time is equal,
w/20=105/35
w=60 workmen
E

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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08 Jul 2017, 02:02
2
KUDOS
Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

This problem could be solved conceptually without calculations

We have 20 worker to produce 35 widgtes in 5 days. In same number of days, we need more worker to produce Three TIMES (105/35 =3) the first situation. So we need 3 Times labor.

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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08 Jul 2017, 02:52
The output has increased but not the number of days, so the number of men should increase linearly.

Since the output has become thrice, the number of men required will be = 20*3 = 60. Ans - E.
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20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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08 Jul 2017, 19:24
First we can derive the rate of one workman as below:
$$20(R)*5=35 => R=\frac{7}{20}$$

Let X be the number of workmen needed and we have the work required (105) and the number of days worked (5) therefore,

$$\frac{X * 7}{20} * 5 = 105 => \frac{35X}{20} = 105 => 35 X = 105 * 20$$ = > divide both sides by 35 => $$x = 3*20 = 60$$

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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12 Jul 2017, 15:30
1
KUDOS
Expert's post
Bunuel wrote:
20 workmen can make 35 widgets in 5 days. How many workmen are needed to make 105 widgets in 5 days?

(A) 7
(B) 20
(C) 25
(D) 30
(E) 60

We are given that the rate of 20 workmen is 35/5 = 7 widgets per day. We need to determine how many workmen are needed for a rate of 105/5 = 21 widgets per day. We can let x = the number of workman and create the following proportion:

20/7 = x/21

(20)(21) = 7x

(20)(3) = x

60 = x

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed [#permalink]

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05 Dec 2017, 11:55
1
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Expert's post
Hi All,

When dealing with these types of 'work' questions, it can be helpful to think in terms of the total amount of work that needs to be done to complete the given task. We're told that it takes 20 workmen 5 days to complete the task. That's...

(20 men)(5 days each) = 100 work-days of effort to create 35 widgets.

Thus, there are a number of different ways to complete that work:
1 worker can work for 100 days
2 workers can work for 50 days each
4 workers can work for 25 days each
Etc.

The question asks us to create 105 widgets, which is 3 times the 35 in the above calculation. Those 105 widgets would take 3(100) = 300 work-days of effort. If we have to complete the job in 5 days, then we can set up the following equation:

(X men)(5 days each) = 300 work-days

X = 60 men

[Reveal] Spoiler:
E

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Re: 20 workmen can make 35 widgets in 5 days. How many workmen are needed   [#permalink] 05 Dec 2017, 11:55
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# 20 workmen can make 35 widgets in 5 days. How many workmen are needed

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