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The output of a factory is increased by 10% to keep up...

by swerve » Tue Jan 30, 2018 6:04 am
The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?

A. 20%
B. 24%
C. 30%
D. 32%
E. 79%

The OA is B.

If original production is P,

First increase by 10% will be, 1.1*P

Second increase by 20% will be, 1.2*1.1*P

Now, how can I determine the decreased to restore the original output? Experts, I need your help. Thanks.
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by GMATGuruNY » Tue Jan 30, 2018 6:18 am
swerve wrote:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?

A. 20%
B. 24%
C. 30%
D. 32%
E. 79%
Let the original output = 100 units.
After a 10% increase, the new output = 100 + (10% of 100) = 100 + 10 = 110 units.
After an additional 20% increase, the resulting output = 110 + (20% of 110) = 110 + 22 = 132 units.
To return to the original output of 100 units, the resulting output must decrease by 32 units.
Percent decrease from 132 to 100 = (difference)/(bigger) = 32/132 = 16/62 ≈ 15/60 = 1/4 = 25%.
Only B is viable.

The correct answer is B.
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by Scott@TargetTestPrep » Wed Jan 31, 2018 4:19 pm
swerve wrote:The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?

A. 20%
B. 24%
C. 30%
D. 32%
E. 79%
Let's say the original output is n; after the increases, the new output is:

1.1 x 1.2 x n = 1.32n = (132/100)n

To reduce (132/100)n back to n, we must multiply by 100/132 since 132/100 x 100/132 = 1.

100/132 = 50/66 = 25/33 ≈ 76%

Thus we have to reduce the new output by 100% - 76% = 24% to restore the original output.

Answer: B

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