MIXTURE AND ALLEGATION

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Always keep in mind the following

1/8 = 12.5% | 1/5 = 20% | 1/4 = 25%

3/8 = 37.5% | 2/5 = 40% | 1/8 = 12.5%

5/8 = 62.5% | 3/5 = 60% | 1/16 = 6.25%

7/8 = 87.5% | 4/5 = 80% | 1/32 = 3.125%

1/9 = 11.11% | 1/11 = 9.09% |

2/9 = 22.22% | 2/11 = 18.18% |

3/9 = 33.33% | 3/11 = 27.27% |

4/9 = 44.44% | 4/11 = 36.36% |

5/9 = 55.55% | 5/11 = 45.45% |

6/9 = 66.66% | 6/11 = 54.54% |

7/9 = 77.77% | 7/11 = 63.63% |

8/9 = 88.88% | 8/11 = 72.72% |

1/7 = 14.28%

2/7 = 28.57%

3/7 = 42.85%

4/7 = 57.14%

5/7 = 71.42%

6/7 = 85.71%

7/7 = 100%

1) The ratio of milk and water in a mixture is 3 : 5. We added 10 lt water to the mixture then ratio becomes
3 : 7. Find the initial quantity of milk.

2) The ratio of milk and water in a  mixture is 3 : 7. We added 10 lt water to the mixture then ratio becomes
1 : 3. Find the initial quantity of milk.

3) The ratio of milk and water in a mixture is 7 : 5. We withdraw 9 lt mixture and added same quantity of water to the mixture, then ratio becomes 1 : 1. Find the initial quantity of milk.

4) The ratio of milk and water in a mixture of 66 lt is 5: 6. We added 12 lt water to the mixture, then find the ratio of milk and water.

5)  The ratio of milk and water in a mixture of 80 lt is 9 : 7. We added 12.5 lt milk to the mixture, then find the ratio of milk and water.

6) The ratio of milk and water in a mixture is 7 : 5. We withdraw 9 lt mixture and added same quantity of water to the mixture, then ratio becomes 7 : 9. Find the initial quantity of milk.

7) The ratio of milk and water in a mixture is 7 : 5. We withdraw 9 lt mixture and added same quantity of water to the mixture, then ratio becomes 1 : 1. Find the initial quantity of milk.

8) The ratio of milk and water in a mixture is 3 : 1. We withdraw 6 lt mixture and added same quantity of water to the mixture, then ratio becomes 9 : 5. Find the initial quantity of milk.

9) The ratio of milk and water in a mixture is 3 : 2. We withdraw 25 lt mixture and added 15 lt water to the mixture, then ratio becomes 3 : 7. Find the initial quantity of milk.

10) The ratio of milk and water in a mixture is 3 : 8. We added x lt of milk to the mixture then ratio becomes 5 : 4 and we added 18 lt water to the mixture, then ratio becomes 4 : 5. Find the value of x.

11)  There is milk and water in a certain ratio in a vessel. If we took out 16 lt water, then the ratio become 3 :4. Then 35 lt milk is taken out , then the ratio becomes 2 : 5. Find the initial quantity of water.

12) There is a mixture of milk and water 120 lt .  1/6 th  part of this mixture is milk. We took out 30 lt mixture and added 'p' lt milk to this mixture and the ratio was reversed. Then we added 'q' lt water to this mixture then again the ratio was reversed. Find the value of (q –p).

13) The ratio of milk and water in a mixture is 3 : 1. How much fraction of the mixture must be drawn off
and substituted by water so that the ratio of milk and water in the mixture becomes 1 : 1?

14) The ratio of milk and water in a mixture is 5 : 3. How much fraction of the mixture must be drawn off
and substituted by water so that the ratio of milk and water in the mixture becomes 1 : 1?

15)  The ratio of milk and water in a mixture is 11 : 7. How much fraction of the mixture must be drawn off 

and substituted by water so that the ratio of milk and water in the mixture becomes 1 : 1?


16)  The ratio of milk and water in a mixture is 2 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of milk and water in the mixture becomes 5 : 3?

17) In a mixture, the ratio of milk to water is 5:3. When 10 litres of milk and 20 litres of water are added in the mixture, then the ratio becomes 6:5. What is the quantity (in litres) of milk in the initial mixture?

18) A mixture contains milk and water in the ratio of 5:1. Adding 5 L of water changes the ratio to 5:2. What was the quantity of milk in the original mixture?

19) A vessel contains milk and water in the ratio of 4:3. If 14 litres of the mixture is drawn and filled with water , the ratio changes to 3:4. How much milk was there in the vessel initially?

20)  A jar contains a mixture of two liquids A and B in the ration $4:1$. When $10$ liters of the mixture is replaced with liquid B the ratio now becomes $2:3$. The volume of liquid A present in the jar earlier was

A .

$20$ litres

B .

$10$ litres

C .

$16$ litres

D .

$15$ litres

21) A tank was full of pure milk. Half of milk was sold

and then the tank was refilled with water. Again half

of milk (mixture) was sold and the tank was refilled

with water and now for the third time half of milk

was sold and tank was refilled with water. In the last

what will be the percentage of milk?

22). In three alloys A, B and C the percentage of copper is 80%, 75% and 70% respectively and the percentage of tin is 15%, 15% and 25% respectively and the remaining is nickel. If 10 kg, 15 kg and 50 kg of the three alloys be mixed together, find the ratio of copper, tin and nickel in the mixture thus obtained.

23).     In a vessel two medicine A and B are in the ratio 4 : 1. 10 lt of mixture is taken out and replaced with 10 lt of medicine B and the ratio of A and B thus becomes 2 : 3. Find the initial quantity of medicine A.

Ans.    16 lt