The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

Alligation or Mixture problems
The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

5 : 7

4 : 7

1 : 1

4 : 9

5 : 7

4 : 7

1 : 1

4 : 9

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Alligation or Mixture problems
A container is full of milk. One-third of milk is taken out of it and replaced by same quantity of water. Then again one-third of the mixture is taken out of it and replaced by the same quantity of water. The process is repeated 4 times. If 16 litres of milk is left in the container at the end of 4th operation, find the capacity of the container.

82 litres

81 litres

76 litres

85 litres

82 litres

81 litres

76 litres

85 litres

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Alligation or Mixture problems
A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?

42 litres

18 litres

24 litres

32 litres

42 litres

18 litres

24 litres

32 litres

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Alligation or Mixture problems
In a 100 litre of mixture the ratio of milk and water is 6:4. How much milk must be added to the mixture in order to make the ratio 3 : 1?

60

45

55

85

60

45

55

85

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Alligation or Mixture problems
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

1 3

1 5

1 7

1 4

1 3

1 5

1 7

1 4

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Alligation or Mixture problems
In what ratio should milk and water be mixed so that after selling the mixture at the cost price a profit of 50/3 % is made?

6:1

2:5

1:2

2:3

6:1

2:5

1:2

2:3

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Method 1 to solve the equation.Let us assume Cost Price (C.P) of 1 liter milk be Y rupees.According to question,Selling Price (S.P) of 1 liter of mixture Y rupees. (Selling price should be same as Cost price)Profit = 50/3 %Let us assume Cost price of 1 Liter of Mixture of Water and Milk = CCost price of 1 Liter of Mixture of Water and Milk = Selling price of Mixture - Profit C = Y - C x 50/3%? C = Y - C x 50/3x100? C = Y - C x 1/3x2? C = Y - C/6? Y = C + C/6? Y = (6C + C)/6? Y = (6C + C)/6? Y = 7C/6? C = 6Y/7Since in Y rupees we will get 1 liter milk.Hence in 1 rupees we will get 1/Y liter milk.Hence in 6Y/7 rupees we will get 1 x 6Y/7 x Y liter milk.Hence in 6Y/7 rupees we will get 6/7 liter milk.We need 1 liter mixture of milk and water for sold on the same price, we need to mix the water.So water quantity in mixture = 1 - 6/7 = 1/7Ratio of Milk and water in mixture = quantity of Milk in Mixture/quantity of Water in MixtureRatio of Milk and water in mixture = 6/7 / 1/7Ratio of Milk and water in mixture = 6 x 7 / 7 Ratio of Milk and water in mixture = 6 / 1Ratio of Milk and water in mixture = 6 : 1Method 2 to solve the question.Let the original amount of milk be 1 liter and the cost price is 1 rupees per liter.Cost price of milk = 1 rupees.Selling price of Mixture = 1 rupees. When the milk is mix with x liters of water milk remaining is 1- x.Let us assume the cost price of milk in mixture is Y and given that the Sold Price is 1.we should use the Profit formula in algebra,Y + Y x 50/3 % = 1 Y + Y x 50/3 x 100 = 1Y + Y x /3 x 2 = 17Y/6 = 1Y = 6/7Y = 6/7 is the cost price of Mixture for 1 liter. Since water is free so there is not cost of water in mixture. So price of milk is 6/7 rs in mixture.Since as per question,In 1 rupees we will get 1 liter of milk.hence in 6/7 rupees we will get 1 x 6/7 = 6/7 liter of milk.Now we have to make 1 liter of mixture with water and milk.quantity of Water + Quantity of Milk = 1 literquantity of Water + 6/7 = 1 quantity of Water = 1 - 6/7 = (7 - 6)/7 quantity of Water = 1/7 Ratio of milk and Water = Quantity of Milk / quantity of Water Ratio of milk and Water = (6/7) / (1/7)Ratio of milk and Water = (6/7) x (7/1)Ratio of milk and Water = 6 x 7/ 7 x 1Ratio of milk and Water = 6 :1

Alligation or Mixture problems

Alligation or Mixture problems The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

Alligation or Mixture problems A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?

Alligation or Mixture problems In a 100 litre of mixture the ratio of milk and water is 6:4. How much milk must be added to the mixture in order to make the ratio 3 : 1?

Alligation or Mixture problems A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Alligation or Mixture problems In what ratio should milk and water be mixed so that after selling the mixture at the cost price a profit of 50/3 % is made?

Alligation or Mixture problems
The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

Alligation or Mixture problems
A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?

Alligation or Mixture problems
In a 100 litre of mixture the ratio of milk and water is 6:4. How much milk must be added to the mixture in order to make the ratio 3 : 1?

Alligation or Mixture problems
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Alligation or Mixture problems
In what ratio should milk and water be mixed so that after selling the mixture at the cost price a profit of 50/3 % is made?