M43-09

Official Solution:

­On a certain day, a coffee shop started selling a batch of freshly baked cookies at a price 20 percent higher than the shop's cost per cookie, selling \(\frac{3}{5}\) of them at that price. By noon, due to high demand, the shop increased the price by an additional 25 percent and sold half of the remaining cookies at the new price. In the evening, to clear out the rest, the shop reduced the price by 20 percent and sold \(\frac{3}{4}\) of the remaining cookies. What was the coffee shop's gross profit from the sale of the cookies as a percentage of its total cost for the batch of baked cookies on that day?

A. \(18\%\)
B. \(20\%\)
C. \(25\%\)
D. \(26 \frac{6}{19}\%\)
E. \(30\%­\)


Let the total number of cookies be 100 (for simplicity) and let the cost per cookie be C.

Initial Cost and Sales

• Initial selling price per cookie is 20% higher than the cost: 1.2 * C.

• Number of cookies sold initially: 3/5 of 100 = 60.

• Revenue from initial sales: 60 * 1.2 * C = 72C.

First Price Increase and Sales:

• Remaining cookies: 100 - 60 = 40.

• New selling price is 25% higher than the initial selling price: 1.2 * C * 1.25 = 1.5 * C.

• Number of cookies sold at the new price: 1/2 of 40 = 20.

• Revenue from sales at the new price: 20 * 1.5 * C = 30C.

Price Decrease and Final Sales:

• Remaining cookies: 40 - 20 = 20.

• Final selling price is 20% less than the previous price: 1.5 * C * 0.8 = 1.2 * C.

• Number of cookies sold at the final price: 3/4 of 20 = 15.

• Revenue from sales at the final price: 15 * 1.2 * C = 18C.

Total Revenue and Total Cost:

• Total revenue: 72C + 30C + 18C = 120C.

• Total cost for the batch of cookies: 100 * C = 100C.

• Gross profit: Total revenue - Total cost = 120C - 100C = 20C.

Profit as a Percentage of Total Cost:

• Gross profit percentage = (Gross profit / Total cost) * 100.

• Gross profit percentage = (20C/100C) * 100 = 20%.


Answer: B