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

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.
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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%

Answer: C

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

Answer C

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 \(=(\frac{17}{8} - 1) * 100 = \frac{9}{8} * 100 = 9 * 12.5 = 112.5%\)

Correct answer is Option C.

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