A vessel, full of water, weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of empty vessel.

Alligation or Mixture problems
A vessel, full of water, weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of empty vessel.

5 kg

8 kg

4 kg

3 kg

5 kg

8 kg

4 kg

3 kg

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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?

2:5

2:3

6:1

1:2

2:5

2:3

6:1

1:2

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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
One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

21 %

26 %

29 %

27 %

21 %

26 %

29 %

27 %

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Alligation or Mixture problems
Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?

3 : 2

2 : 1

2 : 3

1 : 2

3 : 2

2 : 1

2 : 3

1 : 2

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Alligation or Mixture problems
The average monthly salary of employees, consisting of officers and workers, of an organisation is Rs. 3000. The average salary of an officer is Rs. 10,000 while that of a worker is Rs. 2000 per month. If there are total 400 employees in the organisation, find the number of officers and workers separately.

50 , 350

250 , 150

310 , 90

300 , 100

50 , 350

250 , 150

310 , 90

300 , 100

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Alligation or Mixture problems
A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?

70

220

55

110

70

220

55

110

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Alligation or Mixture problems

Alligation or Mixture problems A vessel, full of water, weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of empty vessel.

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 One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

Alligation or Mixture problems Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?

Alligation or Mixture problems A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?

Alligation or Mixture problems
A vessel, full of water, weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of empty vessel.

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
One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

Alligation or Mixture problems
Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?

Alligation or Mixture problems
A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?