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This is true when:
The different amounts are all equal

Example: Assuming that the cost of ingredients, the price sold at, and the amount of drinks made are the same.

Stall A and B both made 100 drinks
Stall A sold 50 drinks -> 50%
Stall B sold 90 drinks -> 90%

Stall A's profit = 50-50=0 drinks worth
Stall B's profit = 90-10=80 drinks worth

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It is false as the prce

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It is false when Stall A sells their drink at the lowest price and highest price for the ingredients, followed by Stall B, then Stall C. For example, if Stall A sells its drink at $25 and its material is $24, Stall B sells it at $60 and its ingredients is $20, and Stall C sells it at $100 and its ingredients is at $10, Stall A will earn $1⨉175=$175, Stall B will earn $40⨉187= $5610 and Stall C will earn $90⨉180=$16200. Therefore, with this information, what Joseph says is false.

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For example, stall B
Drink cost: $1
Ingredients cost: $0.50
Number of drinks sold: 180
Percentage of drinks sold: 85%
Number of drinks unsold: 45
Total profit: 0.5x180-0.5x45=$67.5
While stall C
Drink cost: $2
Ingredients cost: $1
Number of drinks sold: 160
Percentage of drinks sold: 80%
Number of drinks unsold: 40
Total profit: 1x160-1x40=$120

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It is not true when the prices of the drinks are different. For example, Stall A sold 200 out of 230 made drinks, but their drinks cost $0.10. However, Stall B sold 150 out of 200 drinks, but their drinks cost $1.

200 x $0.10 = $20
150  x $1       =$150

30 x $0.10 = $3
50 x $1 = $50

$20 - $3 = $17
$150 - $50 = $100

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It is true when
– The amount of money it took to make the drinks and run the stalls are less than or equal to the other stalls
–The cost of each drink is equal to or more than other stalls

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It is not true when:
The starting amount is different and could also be affected by the selling price, amount sold, and ingredient price.

Example: Assuming the same price and cost of raw ingredients, but with different number of drinks prepared. If stall A prepares 2 drinks and sells both, it sells 100%. If stall B prepares 100 drinks and sells 90, it sells 90%. There would be more profit earned from 50 drinks compared to 2 drinks.
Stall A earns -> 2 Drinks worth
Stall B earns -> 80 Drinks worth

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It is not true when the stall with the highest percentage of drinks sold would earn the most profit
Stall A:
Prepared 20 glasses of water
Sold: 60% of the prepared glasses of water
Price: $10 per glass of water
Stall B:
Prepared 20 glasses of water
Sold: 100% of the prepared glasses of water
Price: $4 per glass of water
Stall A sold 12 glasses of water
12*10=120
Stall B sold 20 glasses of water
20*4=80

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It is not true when the stall with the highest percentage of drinks sold would earn the most profit.

The highest percentage of drinks sold will depend on the amount of drinks prepared, as the amount of drinks prepared are different for each stall A, B, and C. 200, 220, 225 respectively.

Even if they have the same amount of drinks prepared, the prices for each cups might be different.

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This scenario is true if all the stalls have the same base (the total number of glasses prepared at first) and same selling price and cost price.

For example,

All the stall prepares 200 drinks at first, the percentage would show that Stall A sold 87.5% of that 200, which gives us the bigger profit

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It is true when the cost and price of each drinks are all the same.
Eg.
Price of drink: $1
Cost of drink: $0.50

Stall A
Percentage: 87.5% (HIGHEST)
Profit: $87.50 - $25
= $62.50

Stall B
Percentage: 85%
Profit: $93.50 - $33
= $60.20

Stall C
Percentage: 80%
Profit: $90 - $45
= $45

Highest percentage: Stall A
Highest profit: Stall A

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It is true when the cost of the drinks sold by Stall A is higher than Stall B and C and the cost of making the drinks are the same.
Example:
Stall A - $5
Stall B - $3
Stall C - $2

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For example:
Stall A
Drink = $1
Ingredients = $0.50
Drinks prepared = 100
Drinks sold = 90
Percentage sold = 90%

Total cost = $0.50 x 100 = $50
Total earned = $1 x 90 = $90
Profit = $90 - $50 = $40

Stall B
Drink = $1
Ingredients = $0.50
Drinks prepared = 200
Drinks sold = 90
Percentage sold = 45%

Total cost = $0.50 x 200 = $100
Total earned = $1 x 90 = $90
Profit = $90 - $100 = $(-10)

Stall A percentage sold > Stall B percentage sold
Stall A Profit > Stall B Profit

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It is NOT true as

Even though the percentage is higher, when multiplied by a smaller number of drinks, the profit would be lower.

From the info given, stall A sold the highest percentage of glasses. However, they did not sell the most number of glasses, and depending on the prices of the drinks, stall B, which sold the most drinks, could still be the one who earns less profit.

Prices may differ betwixt the stores.

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For example, stall A
Drink cost: $3
Ingredients cost: $1
Number of drinks sold: 175
Percentage of drinks sold: 87.5%
Number of drinks unsold: 25
Total profit: 2x175-1x25=$275
While stall B
Drink cost: $2
Ingredients cost: $1
Number of drinks sold: 187
Percentage of drinks sold: 85%
Number of drinks unsold: 33
Total profit: 1x187-1x33=$164

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This will be true if selling price of drinks in A is higher than selling price of drinks in B and C and selling price of drinks in B is higher than selling price of drinks in C.
Example:
A;$7
B;$4
C;$2

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It is true when Stall A sells their drink at the highest price and lowest price for the ingredients, followed by Stall B, then Stall C. For example, if Stall A sells its drink at $100 and its material is $10, Stall B sells it at $50 and its ingredients is $20, and Stall C sells it at $25 and its ingredients is at $24 , Stall A will earn $90⨉175=$15750, Stall B will earn $30⨉187= $5610 and Stall C will earn $1⨉180= $180. Therefore, with this information, what Joseph says is true.

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It is not true if the total glasses prepared is lesser than the other stalls.