Aptitude Shortcuts and Tricks for Allegation & Mixture Problems

Type-1: If a mixture contains two liquids in the ratio a:b and if x liter of b is added to the mixture, then the ratio of two liquids becomes a:c, then the quantity of liquid in the mixture is given by
[ax/(c-b)] and that of liquid b is given by [bx/(c-b)].

Example: A mixture contains milk and water in ratio 4:3. If 5 litres of water is added to the mixture. The ratio becomes 4:5. The quantity of milk [(4×5)/(5-3)]= 20/2= 10 litre.

Type-2:A container initially contains x unit of liquid and a unit of liquid is taken out and it is filled with a unit of water repeatedly up to n times, then the final quantity of the original liquid in the container is given as

Example: A container has 60 litres of milk, from this container, 4 litres of milk is taken out and replaced with water. If this process is repeated 3 times, then the quality of milk in the container is left.

Type-3:A Container has milk and water in the ratio a:b, a second container has milk and water in the ratio c:d. If both the mixture is emptied into a third container, then the ratio of milk to water in the third container is given by

Example: 3 Container has milk and water in the ratio 2:1, 3:1, 3:2 respectively and all three containers are emptied into a bigger container, the ratio of milk to water in a bigger container.