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12 Jul 2024, 07:00
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B
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Difficulty:
75%
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Question Stats:
70% (03:04) correct
30%
(03:29)
wrong
based on 551
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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 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 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 6/19%
E. 30%
A. 18%
B. 20%
C. 25%
D. 26 6/19%
E. 30%
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12 Jul 2024, 08:15
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Bunuel
GMAT Club Official Explanation:
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.
General Discussion
12 Jul 2024, 07:41
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Let's denote the total number of cookies baked as N and the cost per cookie as C.
Initial Price
The initial selling price per cookie was set at 20% higher than the cost:
P1=C×1.20
Selling at the Initial Price
The shop sold 3/5 of the cookies at the initial price:
Cookies sold= 3/5 N
Revenue from these cookies=3/5 N×P1= 3/5 N×1.20C= 3/5 ×1.20CN=0.72CN
Remaining Cookies
After selling 3/5 of the cookies, the remaining cookies were:
N remaining =N− 3/5 N= 2/5 N
Increased Price
By noon, the shop increased the price by an additional 25%:
P2 = P1×1.25=1.20C×1.25=1.50C
Selling at the Increased Price
The shop sold half of the remaining cookies at the increased price:
Cookies sold= 1/2 × 2/5 N= 1/5 N
Revenue from these cookies= 1/5 N×P2 = 1/5 N×1.50C=0.30CN
Remaining Cookies
After selling half of the remaining cookies, the remaining cookies were:
N remaining = 2/5N− 1/5 N= 1/5 N
Reduced Price
In the evening, the shop reduced the price by 20% to clear out the rest:
P3=P2×0.80=1.50C×0.80=1.20C
Selling at the Reduced Price
The shop sold 3/4 of the remaining cookies at the reduced price:
Cookies sold= 3/4 * 1/5 N
Revenue from these cookies=3/20𝑁×𝑃3
Revenue from these cookies=3/20 N×1.20C=0.18CN
Total Revenue
The total revenue from all sales is the sum of the revenues from each phase:
Total Revenue=0.72CN+0.30CN+0.18CN=1.20CN
Total Cost
The total cost of the batch of cookies is:Total Cost=N×C=CN
Gross Profit
The gross profit is the total revenue minus the total cost:
Gross Profit=Total Revenue−Total Cost=1.20CN−CN=0.20CN
Gross Profit as a Percentage of Total Cost
The gross profit as a percentage of the total cost is:
(0.20𝐶𝑁)/𝐶𝑁×100%=20%
0.20 ×100%=20%
Therefore, the coffee shop's gross profit from the sale of the cookies as a percentage of its total cost for the batch is:20%
Initial Price
The initial selling price per cookie was set at 20% higher than the cost:
P1=C×1.20
Selling at the Initial Price
The shop sold 3/5 of the cookies at the initial price:
Cookies sold= 3/5 N
Revenue from these cookies=3/5 N×P1= 3/5 N×1.20C= 3/5 ×1.20CN=0.72CN
Remaining Cookies
After selling 3/5 of the cookies, the remaining cookies were:
N remaining =N− 3/5 N= 2/5 N
Increased Price
By noon, the shop increased the price by an additional 25%:
P2 = P1×1.25=1.20C×1.25=1.50C
Selling at the Increased Price
The shop sold half of the remaining cookies at the increased price:
Cookies sold= 1/2 × 2/5 N= 1/5 N
Revenue from these cookies= 1/5 N×P2 = 1/5 N×1.50C=0.30CN
Remaining Cookies
After selling half of the remaining cookies, the remaining cookies were:
N remaining = 2/5N− 1/5 N= 1/5 N
Reduced Price
In the evening, the shop reduced the price by 20% to clear out the rest:
P3=P2×0.80=1.50C×0.80=1.20C
Selling at the Reduced Price
The shop sold 3/4 of the remaining cookies at the reduced price:
Cookies sold= 3/4 * 1/5 N
Revenue from these cookies=3/20𝑁×𝑃3
Revenue from these cookies=3/20 N×1.20C=0.18CN
Total Revenue
The total revenue from all sales is the sum of the revenues from each phase:
Total Revenue=0.72CN+0.30CN+0.18CN=1.20CN
Total Cost
The total cost of the batch of cookies is:Total Cost=N×C=CN
Gross Profit
The gross profit is the total revenue minus the total cost:
Gross Profit=Total Revenue−Total Cost=1.20CN−CN=0.20CN
Gross Profit as a Percentage of Total Cost
The gross profit as a percentage of the total cost is:
(0.20𝐶𝑁)/𝐶𝑁×100%=20%
0.20 ×100%=20%
Therefore, the coffee shop's gross profit from the sale of the cookies as a percentage of its total cost for the batch is:20%
