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Over the course of a year, a certain microbrewery increased its beer

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Over the course of a year, a certain microbrewery increased its beer [#permalink]

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02 Dec 2014, 09:10
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4
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Difficulty:

45% (medium)

Question Stats:

67% (01:26) correct 33% (01:19) wrong based on 147 sessions

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Tough and Tricky questions: Percents.

Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?

A) 50%
B) 90%
C) 112.5%
D) 210%
E) 212.5%

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: Over the course of a year, a certain microbrewery increased its beer [#permalink]

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02 Dec 2014, 10:27
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2
Beware of this question's wording...

Let's take the original output to be 100 and the new output to be 170% or 170.
Let's take the original work hours to be 100 hours and the new work hours to be 80% or 80 hours.

The old output per work hour = 100/100 hours or 1.
The new output per work hour = 170/80 or 2.125. So the resulting increase is actually new minus old or 1.125 or 112.5%. Choice C
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Re: Over the course of a year, a certain microbrewery increased its beer [#permalink]

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02 Dec 2014, 19:44
1

Time ........................... Rate .................. Work Done

100 ............................. 1 ............................. 100 (Assumption/ Original Values)

80 ......................... $$\frac{170}{80}$$ ........................ 170 (Output increase by 70%)
(Time decrease by 20%)

Per cent increase in rate $$= (\frac{17}{8} - 1) * 100 = \frac{9}{8} * 100 = 112.5%$$
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Re: Over the course of a year, a certain microbrewery increased its beer [#permalink]

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27 Nov 2017, 19:07
Bunuel wrote:

Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?

A) 50%
B) 90%
C) 112.5%
D) 210%
E) 212.5%

We can let the old output per hour = m, the working hours = w, and n = the percentage increase in output per hour. Thus:

1.7mw = (0.8w)(m)(100 + n/100)

17/10 = (4/5)(100 + n)/100

170 = (4/5)(100 + n)

850 = 400 + 4n

450 = 4n

112.5 = n

Alternate Solution:

Let’s assume that the original output was 100 bottles in 50 hours. This would yield an output of 100 bottles/50 hours = 2 bottles/hour.
.
At the end of the year, the number of bottles was increased by 70%, which is 70 bottles, so the new output is 170 bottles. The total time was decreased by 20%, so the new time is 40 hours. Thus, the new output is 170 bottles/40 hours = 4.25 bottles/hour.

Using the formula percent increase = (new – old)/old x 100%, we have:

(4.25 – 2)/2 x 100% = 2.25/2 x 100% = 112.5%

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Over the course of a year, a certain microbrewery increased its beer [#permalink]

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30 Nov 2017, 10:54
Bunuel wrote:

Tough and Tricky questions: Percents.

Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?

A) 50%
B) 90%
C) 112.5%
D) 210%
E) 212.5%

Kudos for a correct solution.

Source: Chili Hot GMAT

Above poster is right; wording can be tricky. I finally just wrote out the equation.

Output per hour =$$\frac{TotalOutput}{TotalHours}$$

Let original total output = 100
Let original total hours = 10
Original output per hour: $$\frac{100}{10}= 10$$

Total output increases by 70%; new output = 170
Total hours decrease by 20 percent; new hrs = 8
New output per hour: $$\frac{170}{8} = 21.25$$

Percent increase:
$$\frac{Old-New}{Old} * 100 =$$

$$\frac{(21.25-10)}{10} * 100 =$$

$$(\frac{11.25}{10}=1.125 * 100= 112.5$$ percent

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Re: Over the course of a year, a certain microbrewery increased its beer [#permalink]

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30 Nov 2017, 12:39
1
Bunuel wrote:

Tough and Tricky questions: Percents.

Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?

A) 50%
B) 90%
C) 112.5%
D) 210%
E) 212.5%

Kudos for a correct solution.

Source: Chili Hot GMAT

Initial output per hour $$= \frac{N}{H}$$

New Output = N + 70% of N = 1.7N

New Time = H - 20% of H = 0.8H

New output per hour $$= \frac{1.7N}{0.8H} = \frac{17N}{8H}$$

Percent increase in output per hour $$=(\frac{17}{8} - 1) * 100 = \frac{9}{8} * 100 = 9 * 12.5 = 112.5%$$

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Re: Over the course of a year, a certain microbrewery increased its beer   [#permalink] 30 Nov 2017, 12:39
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