It takes 50 identical printing presses 8 hours to print 500,000 papers

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. \(\frac{(50 * 8)}{500000} = \frac{(40 * T_2)}{500000}\)

i.e. \(T_2 = 10\)

Answer: option B

No. of papers to print = \(500,000 * 50 * 8\)

Time taken = \(\frac{500,000 * 50 * 8}{500,000 * 40} = \frac{400}{40} = 10\). Ans (B).

Re: It takes 50 identical printing presses 8 hours to print 500,000 papers [#permalink] New post Jul 21, 2015 10:25 pm
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Bunuel wrote:
It takes 50 identical printing presses 8 hours to print 500,000 papers. How long would it take 40 of these presses to print the same total?

A. 9 hr, 36 min
B. 10 hr
C. 12 hr 24 min
D. 12 hr, 40 min
E. 13 hr, 20 min

Kudos for a correct solution.


50 machines finish the job in 8 hours. We do not have to take care of the 500'000 papers, it does not matter.
40 machines means, 20% less of capacity and therefore 20% longer to work for a certain job.

8 * 1.2 = 9 hr, 36 min

Answer A ..
Hi reto,
since you are looking time for 40 presses it is 25% less so will take 25% more ..
ans 8*1.25=10 hrs..

Thanks chetan2u

I erased my posted, was a bit embarrassing. I don't understand the logic, if you discount from 50 to 40 it is 20%. Why is it that you have to compare 50/40 = Factor 1.25. It is not logical for me.

reto, do not delete your posts as you always learn from your mistakes/gaps in reasoning.

As for your question, you are calculating % wrt 50 and getting 20% while you should actually be looking for % wrt 40 (=10/40= 25%). This is because you need wrt 40 and not wrt 50.

Hope this helps.

Using chain rule,

(50 presses* 8hours)/500,000 papers=(40 presses*x hours)/500,000 papers
Answer 10 hours
B

800score Official Solution:

If it takes 50 presses 8 hours to print 500,000 papers, then it takes 50 × 8 = 400 press-hours to make the total. If there were only 40 presses, and 400 press-hours were needed to print the papers, then each press would need to work for 400/40 = 10 hours to finish the total.

The correct answer is choice (B).

Since the number of papers in both the cases are same we need not consider that part.
50 presses complete a task in 8 hours, therefore 40 presses can complete in 8*50/40 = 10 hours.

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