Bunuel wrote:

A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells.

A. 4:1

B. 5:1

C. 5:2

D. 6:1

E. None of these

Are You Up For the Challenge: 700 Level QuestionsWe can let the ratio of milk to water be 1 : n, and the cost price of 1 gallon of milk is $10. After mixing with water, we have 1 + n gallons of the milk mixture, and he sells every gallon of the mixture for $10.

In the 1 + n gallons of the milk mixture, 1/(1 + n) of it is milk. We can create the equation where x is the number of gallons of milk in 1 gallon of the milk mixture:

x/1 = 1/(1 + n)

x = 1/(1 + n)

So the selling price of milk by the vendor is 10/(1/(1 + n)) = 10(1 + n) per gallon (assuming water does not cost anything) and this is 120% of the cost price of $10 per gallon of milk. We can create the equation:

10(1 + n) = 1.2(10)

1 + n = 1.2

n = 0.2

So for every 1 gallon of milk, the vendor mixed it with 0.2 gallons of water. In other words, for every 5 gallons of milk, the vendor mixed it with 1 gallon of water.

Alternate Solution:

Suppose that the vendor bought 100 gallons of milk for c dollars. If the vendor made a profit of 20%, then it must be true that the vendor made a revenue of 1.2c dollars. Since the vendor sold the milk and water mixture at the same cost per gallon, it follows that the vendor sold 120 gallons of the mixture. Thus, the mixture contains 20 gallons of water for every 100 gallons of milk; which gives us a milk-to-water ratio of 5:1.

Answer: B

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