Working at their respective constant rates, machine A makes 100 copies

Hi All,

This question is essentially just about the two rates involved; as such, the math can be done in a variety of ways (depending on how you want to organize the information).

We're given the rates of 2 machines:
1) Machine A makes 100 copies in 12 minutes
2) Machine B makes 150 copies in 10 minutes.

We're asked for the total number of copies that the two machines will produce in 30 minutes.

30 minutes/12 minutes = 2.5 'sets' of 100 copies
30 minutes/10 minutes = 3 'sets' of 150 copies

(2.5)(100) + 3(150) =
250 + 450 =
700 copies

Final Answer:

GMAT assassins aren't born, they're made,
Rich

rate a= 100/12 copy/min = 25/3 copy/min
rate b = 150/10 copy/min = 15 copy/min

rate a + rate b = rate(ab)

now work done tog = rate(ab) * time ---> (work tog for 30 mins)
work = (25+45)/3 * 30 = 700 copies

Machine A can produce 100 *30/12= 250 copies

And, Machine B can produce 150* 30/10= 450 Copies

Total producing 700 Copies.

D is the answer
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A makes in 12 min 100 copies..so in 1 min it makes 25/3 copies
B makes in 10 min 150 copies..so in 1 min it makes 15 copies

So working together A+B in 1 min makes = 25/3+15 = 70/3 copies

So in 30 min they will make = 30*70/3=700 copies so ans is D

This is a simple question on the concept of Rates.

From the first statement in the question, we can find out the respective rates at which the machines work. Then, we can multiply the rate values with the time to obtain the total work done.

So, the only equation/formula that you need to solve this question is the equation,

Work = Rate * Time

Modifying the above can give us the equation for rate as Rate = \(\frac{Work }{ Time}\).

Rate at which machine A copies = \(\frac{100 }{ 12}\) copies per minute

Rate at which machine B copies = \(\frac{150 }{ 10}\) = 15 copies per minute.

Now, we have been told that each of these machines work independently for 30 minutes; therefore, time = 30 minutes. The number of copies produced by each machine will represent the work done by that machine.

Number of copies produced by machine A = Rate of machine A * Time = \(\frac{100 }{ 12 }\)* 30 = 250

Number of copies produced by machine B = Rate of machine B * Time = 15 * 30 = 450

Therefore, total copies produced by the two machines = 250 + 450 = 700.

The correct answer option is D.
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12 mins 100 copies i.e 60 mins 500 copies
10 mins 150 copies i.e 60 mins 900 copies

i.e 60 mins 1400 copies
i.e 30 mins 700 copies
Option E

I don't like fractional rates and prefer working with easy time parts.

A makes 100 in 12 minutes, so 500 per hour.
B makes 150 in 10 minutes, so 900 per hour.
Together they make 1400 per hour.
So in a half hour, they make 700.

Answer choice D.