The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output

BTGmoderatorDC wrote: ↑

Thu Jul 16, 2020 7:16 pm

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%

OA B

Source: Princeton Review

Say the original output was 100 units; thus, the output after it was increased by 10% = 110; similarly, the output after it was increased by 20% = 110 + 20% of 110 = 132.

So, to reach the original output, we need to reduce the current output by 132 – 100 = 32.

Thus, percentage decrease in output = (32/132)*100% = time-consuming to compute.

Let's find out the approximate value.

Note that 20% of 132 = ~26 < 32. So, the correct answer must be greater than 20%; again, 30% of 132 = ~39 > 32. So, the correct answer must be less than 30%. Thus, the correct answer must be B (= 24%).

Correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Thu Jul 16, 2020 7:16 pm

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%


OA B

Solution:

We can let the original output be 100. Therefore, by the holiday rush, its output is increased to:

100 x 1.1 x 1.2 = 132

Let p be the percent the new output has to be decreased in order to restore to the original output and we can create the equation:

(132 - 100)/132 = p/100

32/132 = p/100

132p = 3200

p = 3200/132 ≈ 24

Answer: B

BTGmoderatorDC wrote: ↑

Thu Jul 16, 2020 7:16 pm

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%


OA B

Source: Princeton Review

Let's plug in some NICE NUMBERS.

Let's say the original output is 100 widgets.
- After a 10% increase the new output = 100 + 10 = 110 widgets
- After a 20% increase the output = 110 + 22 = 132 widgets

We want to get back to the original output.
In other words, we want to decrease from 132 widgets down to 100 widgets.

PERCENT CHANGE = 100(132 - 100 )/132
= 100(32/132)
ASIDE: 32/128 = 1/4 = 25%, so 32/132 must be a LITTLE LESS than 25%.

Take B

Cheers,
Brent