M43-09

Question

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. $30\%$

Show Answer

Official Answer

B

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

Bunuel · Answer

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. $30\%$

Show Answer

Official Answer

B

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

Rebaz · Answer

Bunuel

as a percentage of its total cost for the batch of baked cookies on that day

I get that the  Total cost  is the 100C.

But, what i donot get is the following:

What was the coffee shop's gross profit from the sale of the cookies

Profit= Revenue - Cost. If we run the numbers, we know that the revenue is 120C, but the number of cookies sold( the sale of the cookies ) is 60+20+15= 95 and the cost of these 95 sold cookies is 95C.

My question is, why do you count 100C for the cost of 95 sold cookies to calculate the profit, while the acutal cost for the 95 sold cookies is 95C?

Thanks in advance!

Bunuel · Answer

Not sure what can I add.

gross profit from the sale of the cookies = 120C  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 ?

Total revenue = 120C

The total cost for the batch of  baked cookies on that day  = 100C
 
The coffee shop's gross profit from the sale of the cookies = 20C

BarakYEET · Answer

I think this is a  high-quality  question and I agree with explanation. This is a very long question

Moh12345 · Answer

I solved in a similar way, instead I assigned C = $1. Then we calculating GF, I did in each stage. ex. I did  60 * (1.2*1-1) = $12 for the morning. Eventually I get $25 in profit, which divided by 100(C), where c=$1 gave me 25%. I understand why your way is correct, I was just wondering if you had any idea why my way gave me 5% higher.

braddouglas10 · Answer

I understand your thought process, you're wondering why Bunuel accounts for 100 cookies, not 95 cookies, as the cost. This is because although they didn't sell those last 5 cookies, they still purchased 100 cookies. 100 cookies is the TOTAL cost. They need to still account for the cost of those 5 cookies even though they weren't sold.

If you look at how Bunuel calculated the revenue , he doesn't include the 5 cookies in the 120C, because they were not sold. He only includes the marketed up price.

Since the TOTAL cost was 100C (even though 5 cookies were not sold) and the revenue was 120C (This is the revenue for selling 95 cookies)

Using the percentage change formula, The profit as a percentage of cost is

(Revenue - Cost) /Cost x 100 = 20%

(120 -100) / 100 x 100 = 20%

Hope that helps! Bunuel knows his stuff!

Goldenfuture · Answer

Bunuel  - This took me more than 2 mins - any faster way to do this?

Bunuel · Answer

When I provide a solution, I aim to present an approach that is optimal for this specific question. In that sense, the official solution reflects what I consider the most efficient and reliable method. Also, this is a hard question, so taking slightly more than two minutes is completely reasonable and within expectations. If you are interested, you can also review alternative solution approaches shared here: https://gmatclub.com/forum/gmat-club-ol ... 32394.html

DonBosco7 · Answer

This is certainly not a 2 min question ........ took me at least 4 min

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