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# If 30 machines, each working at the same constant rate, together can p

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Manager
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
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If 30 machines, each working at the same constant rate, together can p  [#permalink]

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24 Jul 2017, 10:09
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Difficulty:

45% (medium)

Question Stats:

77% (02:43) correct 23% (01:51) wrong based on 13 sessions

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If 30 machines, each working at the same constant rate, together can produce $$\frac{n}{2}$$ units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?

A. 30
B. 40
C. 45
D. 50
E. 60

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Senior Manager
Joined: 28 Jun 2015
Posts: 290
Concentration: Finance
GPA: 3.5
Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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24 Jul 2017, 10:24
1
niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce $$\frac{n}{2}$$ units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?

A. 30
B. 40
C. 45
D. 50
E. 60

$$30$$ machines - $$n$$ units - $$30$$ days.

$$x$$ machines - $$2n$$ units - $$30$$ days => $$x = 60$$.

$$y$$ machines - $$2n$$ units - $$45$$ days = $$\frac{30*60}{45} = y = 40$$. Ans - B.
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Senior Manager
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Posts: 331
Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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24 Jul 2017, 10:25
1
Let, Rate of 1 machine = R
Rate of 30 machines = 30R

Work done by 30 machines together for 15 days = 15 * 30R = 450R

Given 30 machines together can produce n/2 units of an item in 15 days

==> 450R = n/2

==> n = 900R

Let number of machines needed to produce 2n units of the item in 45 days = X

==> R * X * 45 = 2n

==> R * X * 45 = 2 * 900R

==> X * 45 = 2 * 900

==> X = 2 * 20 = 40

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If 30 machines, each working at the same constant rate, together can p  [#permalink]

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24 Jul 2017, 10:43
niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce $$\frac{n}{2}$$ units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?

A. 30
B. 40
C. 45
D. 50
E. 60

Let n = 180, n/2 = 90, 2n = 360 (180 is divisible by every number in the prompt)

# of machines * R * T = W

1. 30 machines make 90 units ($$\frac{n}{2})$$ in 15 days

30 * R * 15 = 90

Rate of individual machine = $$\frac{90}{450}$$ ===> $$\frac{1}{5}$$

2. How many machines needed to make 360 units (2n) in 45 days?

(# of machines) * $$\frac{1}{5}$$ * 45 = 360

# of machines = $$\frac{360}{9}$$ = 40

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Joined: 07 Jun 2017
Posts: 10
Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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24 Jul 2017, 10:51
Step 1: Find unit/day of 1 machine.
= n/900 (unit/day)
Step 2: Set Equation
x machines * n/900 (unit/day) * 45 (no. of days) = 2n (targeted units)
x = 40 machines
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Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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26 Jul 2017, 16:36
niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce $$\frac{n}{2}$$ units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?

A. 30
B. 40
C. 45
D. 50
E. 60

We are given that the rate of 30 machines is (n/2)/15 = n/30.

We can create the following proportion to determine the number of machines needed to work at a rate of 2n/45, letting x = the number of machines needed:

30/(n/30) = x/(2n/45)

900/n = 45x/2n

1800n = 45xn

40 = x

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Re: If 30 machines, each working at the same constant rate, together can p   [#permalink] 26 Jul 2017, 16:36
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