In a certain factory, each of workers produces b pairs of shoes every

Question

In a certain factory, each of workers produces  b  pairs of shoes every  c  hours. If  a  workers work around the clock without any breaks, how many days are required to produce 1,000 pairs of shoes?

(A)  \frac{125c}{3ab}

(B)  \frac{1000c}{ab} 
 
(C)  \frac{3a}{125bc}

(D)  \frac{3c}{125ab}

(E)  \frac{125ab}{3c}

Kinshook · Answer

Given: In a certain factory, each of workers produces  b  pairs of shoes every  c  hours. If  a  workers work around the clock without any breaks. 
Asked: How many days are required to produce 1,000 pairs of shoes?

Each worker produces b/c pair of shoes per hour
a workers produce ab/c pair of shoes per hour
For 1000 pair of shoes, time required =  \frac{1000}{(ab/c)} hours = \frac{1000c}{24ab} days=\frac{125c}{3ab}  days

IMO A

CrackverbalGMAT · Answer

This is a classic example of a question where plugging in values will help you solve the problem with the least effort. And that’s something I am going to do in trying to solve this problem.

Let each of the workers produce 5 (b) pairs in 10 (c) hours. This means that each persons makes one pair of shoes in 2 hours. 
Let there be 2 (a) workers. Then, they will produce 10 pairs in 10 hours.

Therefore, to produce 1000 pairs, they will take 1000 hours. 1000 hours is 125/3 days.
Now, from the options, we have to check which option will give us 125 / 3 when we substitute the values of a, b and c.

Clearly, that is option A. The correct answer option is A.

As you see, plugging in simple values is the easiest and the fastest method of solving questions like these. Whenever you have more than a couple of variables to deal with and the answer options are also given in terms of variables, try the plugging in approach.

While plugging in, remember to plug in simple values like 1, 2, 5 , 10, 100 and so on. Of course, there is no mandate on the kind of values that you need to use. Base it on the data given in the question and the expressions/equations you may have formed.

Hope this helps!

Lampard42 · Answer

Sub values and arrive at a value to compare with the values derived from options.

B=2 C=1 and A=1;

Requires 500 hrs to produce 1000 shoes. 500/24=20.something

Only option A gives 20.something. IMO A

Posted from my mobile device

ScottTargetTestPrep · Answer

Each worker makes b pairs in c hours, so the rate of one worker is b/c. Since we have a workers, then their output will be ab/c pairs in c hours.

We have to convert hours to days, so we multiply ab/c by 24 hours per day, obtaining the daily output of the a workers as 24ab/c.

Letting x = the number of days required to make 1,000 pairs of shoes, we can create the equation:

x * 24ab/c = 1000

Solving for x, we obtain:

x = 1000*c/(24ab)

x = 1000c/(24ab)

x= 125c/(3ab)

Answer: A

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In a certain factory, each of workers produces b pairs of shoes every

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