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When the two stalls sell the same drinks for the same price, the drink stall that sells more would earn more money than the drink stall that sold less drinks.

Example:
Stall A sells 75 drinks while stall B sells 50 drinks. The drinks cost $2 each.
Stall A will earn $150 while stall B would only earn $100.

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It is true when the profit(selling price-price used to make the drink) earned from 1 glass is more than the other stall, or if the number of glasses sold is greater than the other stall and the profit earned from 1 glass is less but close enough to the other stall such that they earn more profit, or they have identical profits.
e.g.
Shop A profit=$6-$3=$3
Shop B profit=$5-$3=$2
$3>$2
If shop A sells 50 glasses=$3x50=$150
shop B sells 46 glasses=$2x46=$92
50>46, A sells more glasses than B
$150>$92, so A profit>B profit
OR
Shop A profit=$5.30-$3=$2.30
Shop B profit=$6-$3=$3
$3>$2.30
If shop A sells 50 glasses=$2.30x50=$115
shop B sells 36 glasses=$3x36=$108
50>36, A sells more glasses than B
$115>$108, so A profit>B profit
OR
Shop A profit=$6-$3=$3
Shop B profit=$7-$4=$3
$3=$3, both profits are identical
If shop A sells 50 glasses=$3x50=$150
shop B sells 49 glasses=$3x49=$147
50>49, A sells more glasses than B
$150>$147, so A profit>B profit

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It is false when Stall A sells their drink at the highest price and lowest price for the ingredients, followed by Stall C, then Stall B. For example, if Stall A sells its drink at $100 and its material is $10, Stall B sells it at $25 and its ingredients is $24, and Stall C sells it at $50 and its ingredients is at $20, Stall A will earn $90⨉175=$15750, Stall B will earn $1⨉187= $187 and Stall C will earn $30⨉180=$5400. Therefore, with this information, what Paul says is false.

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It is true when Stall B 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 $25 and its material is $24, Stall B sells it at $100 and its ingredients is $10, and Stall C sells it at $50 and its ingredients is at $20, Stall A will earn $1⨉175=$175, Stall B will earn $90⨉187= $16830 and Stall C will earn $30⨉180= $5400. Therefore, with this information, what Paul says is true.

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For example:

Stall A
Price of drink = $1
Cost of drink = $0.50
Profit per drink = $0.50
Drinks sold = 90
Drinks prepared = 100
Profit = ($1 x 90) - ($0.50 x 100) = $40

Stall B
Price of drink = $10
Cost of drink = $0.50
Profit per drink = $9.50
Drinks sold = 80
Drinks prepared = 100
Profit = ($10 x 80) - ($0.50 x 100) = $750

Profit of B > Profit of A

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It is not true. Even if they sell the most glasses, they may not have made the most money because they may have sold only 10% of their glasses and may even lose money. If the stall sells each cup for $2 but only sell 10% of the total which is 100, even though they may have sold $20 worth, they still lose $80

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It is not true,
A person can sell many drinks for an extremely low price. A peson can also sell lesser drinks but charge at a higher price so the person who charges the high price may earn more money.

(Cheap drink)
e.g $0.50 (price) 100 (quantity)
= $0.50 x 100 = $50

(Expensive drink)
e.g $1.50 (price) 50 (quantity)
= $1.50 x 50 = $75

:D

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the stall sells the glasses at a lower price. if stall A sells each glass for $0.10 and sells 50 glasses but stall B sells each glass for $3 and sells 10 glasses, stall B would still earn more profit

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It is not true if the product of the following values are not the highest among the 3 stalls:
The combined cost of the individual ingredients from the supplier subtracted from the price where the drink is sold
Number of drinks sold

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If the profit of each glass (selling price of cup -  cost of cup) and the amount of prepared cups is constant

shop a --> sellingPrice = 15 cost = 10
preparedCups = 150
profitPerCup= 15-10=5
shop b --> sellingPrice = 12 cost = 7
preparedCups = 150
profitPerCup = 12-7=5

thus, if
A sells 100 cups, while
b]B sells 90 cups,
a initialProfit--> 100*5=500
a totalProfit--> 500-(150-100)*10
b initialProfit--> 90*5=450
b totalProfit--> 450-(150-90)*10
a       b

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It is true when the stall sells more drinks at a higher price.
Example: When stall A sells 100 drinks at $2.00 each and Stall B sells 50 drinks at $1.00 each. Stall A will make $200 and Stall B will only make $100.

It is also true when both of the prices are constant.
Example: Stall C sells 100 drinks at $1.00 each and Stall D sells 200 drinks at $1.00 each. Stall C will make $100 and Stall D will make $200

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It is not true when...
Stall A sells 10 drinks for $1 while stall B sells 18 drinks at $0.50. Both stalls sell the same drink.
In the end stall A earns more than stall B despite stall B selling more drinks.
So the amount of profit earned would be based on the price of the drink in which it is sold at and price of ingredients.

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What Paul says is false when the price of drinks is different.
For example, Stall B sells the most number of glasses but the price is just $1. Stall A sells the least number of glasses but the price is $5.

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When Paul is smart:

If stall B sells drinks at $10000 each and Stall C sells at $10000 each and Stall A also sells drinks at $10000 each, so the statement is true when the price of all drink store's drinks is the same.

When Paul is unsmart:

If Stall B sells 187 drinks and sells it at $2 each and Stall C sells 180 drinks for $3 each and stall A sells 175 drinks for $100000 each, Stall A makes the most profit, followed by Stall C and B

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It is not true when the stall that sells lesser drinks sells them for a higher price. For example, A sold 175 glasses and B sold 187 glasses. If we assume that the drinks cost the same amount to prepare, then A sold their drinks for $2 each and B sold their drinks for $1.50, A would earn $350 while B will only earn $280.50