Problem Solving

BTGmoderatorLU wrote:Source: Economist Gmat

In the "Mashburn" pharmaceutical company there are two machines, a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. "¨If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

A. 13:15
B. 14:15
C. 14:30
D. 15:40
E. 19:15

The OA is B.

Say the daily quota of Red machine is 100 pills; thus, the daily quota of Blue machine would be 100 +20% = 120 pills

Thus, the half of the combined daily quota = 1/2 of (120 + 100) = 110 pills

Given that Blue and Red machines work for 10 hours in a day, the rate of Blue machine = 120/10 = 12 pills/hour = 1/5 pill/min; similarly, the rate of Red machine = 100/10 = 10 pills/hour = 1/6 pill/min

Since Blue machine starts at 8:00 am and Red stars at 10:45 am, Blue machine worked for 2:45 hours (165 minutes) alone, producing 165/5 = 33 pills

From 10:45 am, both the machines work together. Now both the machines together have to produce 110 - 33 = 77 pills

The combined per minute rate of both the machines = 1/5 + 1/6 = 11/30 pills per minute

Thus, time needed to produce 77 pills = 77 / (11/30) = (77*30)/11 = 210 minutes = 3 hours 30 minutes

Thus, time when half the daily is done = 10:45 + 3:30 hours = 14:15 pm.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Economist Gmat

In the "Mashburn" pharmaceutical company there are two machines, a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. "¨If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

A. 13:15
B. 14:15
C. 14:30
D. 15:40
E. 19:15

Let the daily quota for the red machine be 100 pills, so the daily quota for the blue machine is 120 pills. Thus, the combined daily quota is 220 pills.

Since each machine is operated 10 hours a day, the rate of the red machine is 10 pills per hour and the rate of the blue machine is 12 pills per hour. So their combined rate is 22 pills per hour. Therefore, they need to produce a total of 110 pills to satisfy half of the combined daily quota. However, since the blue machine has worked 2 hour 45 minutes before the red machine does, the blue machine has produced 2.75 x 12 = 33 pills. Therefore, when they work together starting at 10:45, they need to produce only 110 - 33 = 77 pills. We can create the following equation where t = the number of hours they work together to produce 77 pills:

22t = 77

t = 77/22 = 7/2 = 3.5

So they will produce half of the combined daily quota by 10:45 + 3.5 hours = 10:45 + 3:30 = 13:75 = 14:15.

Answer: B