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Each machine at a toy factory assembles a certain kind of

by AAPL » Thu Jan 02, 2020 4:10 pm
Official Guide

Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20%
B. 25%
C. 30%
D. 40%
E. 50%

OA A
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by Jay@ManhattanReview » Thu Jan 02, 2020 9:00 pm
AAPL wrote:Official Guide

Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20%
B. 25%
C. 30%
D. 40%
E. 50%

OA A
Say there are 100 machines; thus each of these 100 machines assembles 60/3 = 20 toys in an hour

Thus, in one hour, the 100 machines assemble 20*100 = 2,000 toys.

After the replacement of 40% machines with newer and relatively more efficient ones. So, now there are 60 old and 40 newer machines. Each of these 40 newer machines assembles 60/2 = 30 toys in an hour

1. No. of toys assembled by 60 old machines in 1 hour = 20*60 = 1,200;
2. No. of toys assembled by 40 newer machines in 1 hour = 30*40 = 1,200;

Thus, now, the total no. of toys assembled in one hour = 1,200 + 1,200 = 2,400.

The percent increase in the number of toys assembled in one-hour = [(2,400 - 2,000)/2,000]*100% = 20%

The correct answer: A

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Sat Jan 04, 2020 7:19 pm
AAPL wrote:Official Guide

Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20%
B. 25%
C. 30%
D. 40%
E. 50%

OA A
The rate of one old machine is 20 toys per hour. The rate of one new machine is 30 toys per hour.

Let's assume that there are 10 old machines. So, before any of them are replaced, the number of toys produced in an hour is 10 x 20 = 200.

Since 40 percent of the old machines are replaced with new machines, we have now 6 old machines and 4 new machines, and the number of toys produced in an hour is 6 x 20 + 4 x 30 = 240.

Therefore, the percent increase in the productivity per hour is:

(New - Old)/Old x 100 = (240 - 200)/200 x 100 = 40/200 x 100 = 20 percent

Answer: A

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