Multiple choice

A print shop has N identical printers. Each printer can produce 1 poster every 4 minutes. The shop replaces 40% of the printers with new printers, each of which can produce 1 poster every 2 minutes. All printers operate continuously at their respective rates. By what percent does the total number of posters that can be produced in 1 hour increase as a result of the replacement?

  1. 25%

  2. 33 1 3 %

  3. 40%

  4. 50%

  5. 66 2 3 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let N = 100. Old rate = 100/4 = 25 posters/min. Replace 40% (40 printers) with new ones (rate 1/2). New rate = 60*40/2 + 60*60/4 = 1200 + 900 = 2100 posters/hour. Old rate = 25*60 = 1500 posters/hour. Increase = (2100 - 1500) / 1500 = 600 / 1500 = 40%.

AI explanation

Assume the initial number of printers N is 10 for simplicity, meaning 4 old printers were replaced, leaving 6 old printers and 4 new ones. In 60 minutes, the 6 old printers produce 90 posters, and the 4 new printers produce 120 posters, totaling 210 posters per hour. Originally, 10 printers each producing 1 poster every 4 minutes would yield 150 posters per hour. The increase of 60 posters over the original 150 posters is a 40% increase.

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