Alligation or Mixture Questions

Q:

A vessel is filled with liquid, 3 parts of which are water and 5 parts of 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?

A) 1/3 B) 1/4
C) 1/5 D) 1/7
 
Answer & Explanation Answer: C) 1/5

Explanation:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =  litres.

Quantity of syrup in new mixture =   litres.

 {\color{Blue} \therefore } 

=>   5x + 24 = 40 - 5x 

=>   10x = 16    => x = 8/5

So, part of the mixture replaced =  = 1/5.

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Q:

A can contains a mixture of two liquids A and B in the ratio  7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

A) 10 B) 20
C) 21 D) 25
 
Answer & Explanation Answer: C) 21

Explanation:

Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively

Quantity of A in mixture left = litres.

Quantity of B in mixture left =  litres.

So, the can contained 21 litres of A.

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Q:

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally?

A) 18 litres B) 24 litres
C) 32 litres D) 42 litres
 
Answer & Explanation Answer: B) 24 litres

Explanation:

Let the quantity of the wine in the cask originally be x litres
Then, quantity of wine left in cask after 4 operations =litres

{\color{Black} \Rightarrow 3x-24=2x}

{\color{Black} \Rightarrow x=24}

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Q:

A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A) 400 kg B) 560 kg
C) 600 kg D) 640 kg
 
Answer & Explanation Answer: C) 600 kg

Explanation:

By the rule of alligation:

Profit of first part                         Profit of second part

So, ratio of 1st and 2nd parts = 4 : 6 = 2 : 3. 

{\color{Blue} \therefore } Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg.

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Q:

A container contains 40 litres of milk.From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.

A) 26.34 litres B) 27.36 litres
C) 28 litres D) 29.16 litres
 
Answer & Explanation Answer: D) 29.16 litres

Explanation:

Amount of milk left after 3 operations

 litres

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