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jacob46
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A store sold 60 percent of the hats from a shipment of hats at a 27 Jul 2025, 04:12
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Great explanation, I had a quick follow up question. The mistake I did was take this profit as percentage of only the total cost of sold hats which is like 88. How do i discern if the case is that i have to take the total cost of shipment as base for the percenatge? I noticed that question does not mention it as total cost
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A store sold 60 percent of the hats from a shipment of hats at a selling price that was 50 percent greater than the store's cost for each hat. Then the store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price. If the store did not sell any other hats form the shipment, then the store's gross profit from the sale of the hats from the shipment was what percent of the store's cost for the hats from the shipment?

A) 1%
B) 4%
C) 9%
D) 13%
E) 25%

Choosing the right numbers is very crucial to solve this question.

Let's assume that the number of hats in the shipment = 100

A store sold 60 percent of the hats from a shipment of hats at a selling price that was 50 percent greater than the store's cost for each hat

Number of hats sold = 60

Also given - The initial selling price of the hats = \(\frac{3}{2}\) * times the store's cost for each hat.

Let's assume the stores cost for each hat = $2
Cost price of 100 hats = $2 * 100 = $200

The initial selling price of the hats = \(\frac{3}{2} * 2 = $3\)

Hats remaining = \(100 - 60 = 40\)

Then the store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price.

\(66 \frac{2}{3}\)% \(= \frac{2}{3}\)

New selling price = \(\frac{1}{3}\)rd * old selling price

New selling price = \(\frac{1}{3}\)rd * 3 = $1

Number of hats sold = \(\frac{70}{100} * 40 = 28\)

Total Revenue = (60 * 3) + (28 * 1)= 208

Profit = $(208-200) = $8

Profit % = \(\frac{8}{200} * 100 = 4\)%

Option B
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A store sold 60 percent of the hats from a shipment of hats at a 28 Jul 2025, 10:28
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CashFlowPositive
This question is unfair towards anyone with a financial background as it assumes without stating that the unsold inventory from the shipment would be written down and expensed as part of the costs of goods sold for the purposes of this exercise, which is not obvious at all.
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We can also do it without assuming any numbers:

Let original price of hat = x and total hats in shipment = y

Selling price of hat for 60% of hats = 1.5x

Selling price of hat for 28% of hats (Remaining 40% of hats * 70% of those were sold)= 2/3 of 1.5x= 0.5x

Revenue= 1.5x*0.6y + 0.5x*0.28y = 0.9xy + 0.14xy= 1.04xy

GP = 1.04xy -xy = 0.04xy

GP/Cost % = (0.04xy/xy)*100 = 4%

I think this method helped me avoid the trap of the suboptimal language of the question, which leaves it unclear if unsold inventory is expensed as loss or not.
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A store sold 60 percent of the hats from a shipment of hats at a 01 Aug 2025, 13:00
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Total cost of shipment be - x

60% Of the shipment would cost - 3/5x
Revenue from 60% of shipment would be 3/5x*3/2 = 9/10x

70% of remaining 40% of shipment would cost - 14/50x
Revenue from it would be - 7/50x (3/2* 1/3 = 1/2 - Note that 66 2/3 = 1/3)

Total revenue - 9/10x+7/50x = 52/50x, Profit = 52/50x - x = 2/50x

Profit % = 2/50 x divided by x *100 = 4%
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A store sold 60 percent of the hats from a shipment of hats at a 03 Aug 2025, 02:44
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Hello, people. Let’s get into this. Fair to say this is a bit lengthy but not that tough from a conceptual point of view. You know what you have to do but being extra careful to keep track of what to calculate along the way and not making any careless errors can be helpful.

Looking at the percentages involved, let’s start with a friendly cost price which we can increase by 50% and then decrease by two-thirds without the values becoming hard to use.

Let’s start with a cost price of $10
The original sales price would therefore be $15
And the final sales price would be $5

Similarly, let’s use a friendly value for the number of hats involved: 100 hats

Remember, the final expression we’re looking to put all this into is: [(Total Revenue - Total Cost) / Total Cost] x 100

Total Revenue:

60% of hats were sold at the original sales price -> 60 hats @ $15 = $900

70% of the remaining 40% of hats were sold at the final sales price -> 28 hats @ $5 = $140

Total Revenue = $1040

Total Cost:

100 hats @ $10

Total Cost = $1000


___


We’re nearly there! All we have to do is plug these values into our final expression.

[(Total Revenue - Total Cost) / Total Cost] x 100

[($1040 - $1000) / $1000] x 100

4%

(B) is your answer.
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A store sold 60 percent of the hats from a shipment of hats at a 29 Aug 2025, 08:39
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I reallt like the question & the solution provided. Thanks!
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