GMAT Practice Question: On a certain day, a bakery produced a batch of rolls at a total production cost of 300 dollars....
Question
On a certain day, a bakery produced a batch of rolls at a total production cost of 300 dollars. On that day, \frac{4}{5} of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls?
- $150
- $144
- $132
- $108
- $90
Topics: word problems, percentages, revenue/cost, mean, relative changes, translations
Solution
Step 1
We let N be the total number of rolls and c the average production cost per roll.
c = \frac{300}{N}
Step 2
We translate \textbf{\text{"4/5 of the rolls in the batch were sold"}} into the expression for the rolls sold on day one.
\frac{4}{5}N
Step 3
We express the selling price on day one as 50% greater than the cost per roll.
1.5 \times c
Step 4
We compute the revenue on day one by multiplying the number of rolls sold by the day one price and substituting for c.
R_1 = \frac{4}{5}N \times 1.5 \times c = \frac{4}{5}N \times 1.5 \times \frac{300}{N} = 360
Step 5
We translate \textbf{\text{"20 percent less than the price of the day before"}} into the selling price on day two.
p_2 = 0.8 \times (1.5 \times c) = 1.2 \times c
Step 6
We compute the revenue on day two by multiplying the remaining rolls by the day two price and substituting for c.
R_2 = \frac{1}{5}N \times 1.2 \times c = \frac{1}{5}N \times 1.2 \times \frac{300}{N} = 72
Step 7
We find the profit by subtracting the total production cost from the total revenue.
\text{Profit} = (360 + 72) - 300 = 432 - 300 = 132
Answer
The bakery’s profit was 132, so the correct answer is C.
