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04 Feb 2018, 21:34
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (02:04) correct
38%
(02:06)
wrong
based on 178
sessions
History
Date
Time
Result
Not Attempted Yet
At the Scholarly Text Printing Company, each of n printing presses can produce on the average t books every m minutes. If all presses work without interruption, how many hours will be required to produce a run of 10,000 books?
(A) 10,000*60mn/t
(B) 10,000*60tm/n
(C) 10,000mn/(60t)
(D) 10,000m/(60nt)
(E) 10,000/(60mnt)
(A) 10,000*60mn/t
(B) 10,000*60tm/n
(C) 10,000mn/(60t)
(D) 10,000m/(60nt)
(E) 10,000/(60mnt)
05 Feb 2018, 03:49
Kudos
Bookmarks
Bunuel
Algebraic Method
Since 1 printing press produces t books in m minutes, 1 printing press produces \(\frac{t}{m}\) books in a minute.
In an hour, the printing press will produce \(\frac{60t}{m}\) books. 'n' printing presses would produce \(\frac{60nt}{m}\) books per hour.
Therefore, the presses need \(\frac{10000m}{60nt}\) hours (Option D) to produce 10000 books.
Assuming numbers
1 printing press will produce (t = 10) books in (m = 6) minutes.
Therefore, 1 printing press produces \(\frac{5}{3}\) books in a minute.
In an hour, the printing presses will produce \(60(\frac{5}{3}) = 100\) books.
If there are (n=10) machines to do the work, every hour 1000 books are printed
In order to print 10000 books, it took the n printing presses \(\frac{10000}{1000} = 10\) hours.
Substituting the values of t,m,and n in the answer options,
(A) 10,000*60mn/t = 10000*60*6*10/10 = 3600000 hours
(B) 10,000*60tm/n = 10000*60*10*6/10 = 3600000 hours
(C) 10,000mn/(60t) = 10000*10*10/60*6 = 100000/36 hours
(D) 10,000m/(60nt) = 10000*6/60*10*10 = 10 hours
(E) 10,000/(60mnt) = 10000/60*10*6*10 = 10000/36000 hours (Option D)
05 Feb 2018, 21:06
Kudos
Bookmarks
Bunuel
It should be D
Each press produces \(t\) books every \(m\) minutes --> \(\frac{t}{m}\) = \(\frac{t}{m}*60 \frac{minutes}{hour}\) = \(\frac{60t}{m}\) books per hour
\(n\) presses would make \(\frac{n*60t}{m}\) books per hour.
\(Rate * Time = Work\)
\(Time = Work/Rate\)
\(Time = \frac{10000}{60nt/m}\)
\(Time = 10000m/60nt\)
