Question

A cask contains 12 gallons of mixture of wine and water in the ratio 3 : 1. how much of the mixture must be drawn off and water substituted, so that wine and water in the cask may become half and half.

Answer 1

you can substitute 6 gallons to make it equal
or to make it half you should add 3 gallons water and remove 1 gallon wine

Answer 2

Answer:

4 gallon

Step-by-step explanation:

Total amount of mixture = 12 gallon

ration of wine : water = 3:1

amount of wine = 12* (3/4) = 9 gallon

amount of water = 12* 1/4 = 3 gallon

let x gallon is amount of mixture substituted with water

now,

amount of wine in x gallon = x * 3/4 = 3x/4

amount of water in x gallon = x/4

now,

amount of wine in mixture = 9 - 3x/4

amount of water in mixture = 3 - x/4 + x

as the amount of water and wine is now same.

therefore,

3 - x/4 + x = 9 - 3x/4

x+3x/4 - x/4 = 9-3 = 6

3x/2 = 6

3x = 12

x = 4

therefore 4 gallon of mixture is replaced by 4 gallon of water