Alligation or Mixture Questions

FACTS  AND  FORMULAE  FOR  ALLIGATION  OR  MIXTURE  QUESTIONS

 

 

I. Alligation : It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

 

II. Mean Price : The cost price of a unit quantity of the mixture is called the mean price.

 

III. Rule of Alligation : Suppose Rs.x per unit be the price of first ingradient mixed with another ingradient (cheaper) of price Rs.y per unit to form a mixture whose mean price is Rs. z per unit, then 

Quantity of cheaper : Quantity of dearer

       = ( C.P of dearer - Mean Price ) : ( Mean Price - C. P of cheaper )

       = ( x- z ) : ( z - y )

 

 IV. Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After  operations , the quantity of pure liquid = x1-yxn units.

 

Q:

A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?

A) 3 B) 1
C) 2 D) 4
 
Answer & Explanation Answer: A) 3

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Q:

In what ratio should tea costing Rs 300/kg be mixed with tea costing Rs 200/kg so that the cost of the mixture is Rs 225/kg?

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

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Q:

20 kg of a mixture of wheat and husk contains 5% husk. How many kg more of husk must be added to make the husk content 20% in the new mixture?

A) 2.75 B) 3.75
C) 4.75 D) 5.75
 
Answer & Explanation Answer: B) 3.75

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Q:

In a mixture, unbroken and broken rice grains are in the ratio 3 : 2. How much fraction of the mixture must be drawn off and substituted with broken grains, so that the ratio of unbroken and broken grains becomes 1 : 1?

 

A) 1/3 B) 1/6
C) 1/4 D) 2/5
 
Answer & Explanation Answer: B) 1/6

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Q:

In a mixture of milk and water, there is 19% milk. If the quantity of milk in the mixture is 437 mililitres, then what is the total quantity (in millilitres) of mixture?

A) 2300 B) 2200
C) 2350 D) 2400
 
Answer & Explanation Answer: A) 2300

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Q:

50 litre mixture of water and alcohol contains 10% alcohol. How much more alcohol must be added to make the strength of alcohol 40% in the new mixture?

A) 25 B) 30
C) 20 D) 23
 
Answer & Explanation Answer: A) 25

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Q:

In a triangle XYZ , which of the following conditions is true

A) XY ­ YZ > ZX B) XY + YZ < ZX
C) XY ­ YZ < XZ D) XY + ZX < YZ
 
Answer & Explanation Answer: C) XY ­ YZ < XZ

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Q:

A mixture contains spirit and water in the ratio of 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is

A) 12 litres B) 10 litres
C) 9 litres D) 8 litres
 
Answer & Explanation Answer: C) 9 litres

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