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:

In 250 litres mixture of soda and water the ratio of amount of soda to that of water is 7 : 18. In order to make this ratio 2 : 3, how many more litres of soda should be added?

A) 37.5 B) 42.5
C) 45 D) 50
 
Answer & Explanation Answer: D) 50

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3 1483
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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4 1474
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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2 1386
Q:

In a mixture, ink and water are in the ratio of 8 : 5. If 24 litres of water is added to the mixture, then the new ratio becomes 8 : 11. What is the total quantity (in litres) of water in the new mixture?

A) 40 B) 42
C) 44 D) 48
 
Answer & Explanation Answer: C) 44

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4 1386
Q:

An alloy is made by mixing metal A costing Rs 2000/kg and metal B costing Rs 400/kg in the ratio A:B = 3:1. What is the cost (in Rs) of 8 kilograms of this alloy?

A) 1600 B) 9800
C) 6400 D) 12800
 
Answer & Explanation Answer: D) 12800

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3 1353
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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2 1347
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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5 1288
Q:

Two water-squash mixtures, the first having a water-to-squash ratio of 4 : 1 and the other having a ratio of 3 : 1, are blended in the ratio 1 : 2. What is the water : squash ratio in the blend?

A) 19:11 B) 23:7
C) 17:13 D) 4:3
 
Answer & Explanation Answer: B) 23:7

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