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

Question

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

TimeTraveller · Answer

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.

quantumliner · Answer

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

Answer is B

generis · Answer

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

Answer B

BusyPhilipps · Answer

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

ScottTargetTestPrep · Answer

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

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards