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Alligation or Mixture

Alligation or Mixture: Formulas, Shortcuts and Solved Examples

Alligation is a shortcut for mixing two things that differ in price or strength. It tells…
A container has x units of liquid. If y units are drawn off and replaced with water, and this is repeated n times, what is the correct formula for the pure liquid remaining?
When water (which costs nothing) is mixed with milk, what cost price should be used for water in an alligation calculation?
By the rule of alligation, if a cheaper ingredient costs c and a dearer one costs d, and the mean price of the mixture is m, what is the ratio of cheaper to dearer quantity?
In the rule of alligation, what is the term for the cost price of a unit quantity of the final mixture called?
Vessel A contains milk and water in the ratio 1 : 4, and vessel B contains milk and water in the ratio 1 : 1. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 2 : 3?
Vessel A contains milk and water in the ratio 2 : 5, and vessel B contains milk and water in the ratio 4 : 1. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 3 : 2?
Vessel A contains milk and water in the ratio 1 : 4, and vessel B contains milk and water in the ratio 4 : 5. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 2 : 3?
Vessel A contains milk and water in the ratio 2 : 5, and vessel B contains milk and water in the ratio 5 : 2. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 3 : 2?
Vessel A contains milk and water in the ratio 5 : 1, and vessel B contains milk and water in the ratio 5 : 4. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 3 : 2?
Vessel A contains milk and water in the ratio 1 : 2, and vessel B contains milk and water in the ratio 5 : 3. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 1 : 1?
Vessel A contains milk and water in the ratio 5 : 4, and vessel B contains milk and water in the ratio 2 : 5. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 1 : 2?
Vessel A contains milk and water in the ratio 3 : 5, and vessel B contains milk and water in the ratio 5 : 2. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 2 : 1?
Vessel A contains milk and water in the ratio 5 : 2, and vessel B contains milk and water in the ratio 1 : 4. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 1 : 2?
Vessel A contains milk and water in the ratio 1 : 4, and vessel B contains milk and water in the ratio 2 : 3. In what ratio must liquids from A and B be mixed to get a new mixture with milk and water in the ratio 1 : 2?
A container has 72 litres of pure milk. 24 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 375 litres of pure milk. 300 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 150 litres of pure milk. 120 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 144 litres of pure milk. 24 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 100 litres of pure milk. 20 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 144 litres of pure milk. 72 litres are drawn off and replaced with water. This is done 2 times in total. How much pure milk is left in the container?
A container has 250 litres of pure milk. 200 litres are drawn off and replaced with water. This is done 3 times in total. How much pure milk is left in the container?
A container has 405 litres of pure milk. 135 litres are drawn off and replaced with water. This is done 3 times in total. How much pure milk is left in the container?
A container has 81 litres of pure milk. 27 litres are drawn off and replaced with water. This is done 3 times in total. How much pure milk is left in the container?
A container has 120 litres of pure milk. 60 litres are drawn off and replaced with water. This is done 3 times in total. How much pure milk is left in the container?

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