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 Alligation or Mixture Questions

Popular Latest Rated Important Formulae

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 sum of Rs.118 was divided among 50 boys and girls such that each boy received Rs.2.60 and each girl Rs.1.80. Find the number of boys and girls ?

Answer

Average money received by each = 118/50 = Rs. 2.36 


 


 Therefore, Ratio of No.of boys and girls = 56 : 24 = 7 : 3


 Therefore, Number of boys = 50 x (7/10) = 35


 Number of girls = 50 - 35 = 15

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Subject: Alligation or Mixture

56 26967
Q:

The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

A) 14 and 16 B) 13 and 27
C) 17 and 27 D) None of these
 
Answer & Explanation Answer: B) 13 and 27

Explanation:

Total no.of boys : no. of girls = 13:27

       27             :                13

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69 26826
Q:

A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :

A) 83.33 ml B) 90.90 ml
C) 99.09 ml D) can't be determined
 
Answer & Explanation Answer: A) 83.33 ml

Explanation:

Profit (%) = 9.09 % = 1/11

 

Since the ratio of water and milk is  1 : 11,

 

Therefore the ratio of water is to mixture = 1:12

 

Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

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76 26824
Q:

In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)

A) 80% B) 70%
C) 75% D) 62%
 
Answer & Explanation Answer: A) 80%

Explanation:

Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.

 

After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and weight of a mixture = 60 + 15 = 75 gm.

 

So % of water = 100 x 60/75 = 80%.

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Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

40 26140
Q:

The ratio of water and alcohol in two different containers is 2:3 and 4:5. In what ratio we are required to mix the mixtures  of two containers in order to get the new mixture in which the ratio of alcohol and water be 7:5?

A) 7:3 B) 5:3
C) 8:5 D) 2:7
 
Answer & Explanation Answer: B) 5:3

Explanation:

W1:A1  W2:A2  ..... WN:AN

  2 : 3                   4 : 5                    5 : 7 

 

W1W1+A1 = 25 W2W2+A2=49  WNWN+AN = 512

= 72/180

= 80/180

= 75/180  

                     

 

 =>     5   :   3

 

Therefore, the ratio is  5: 3

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Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Analyst , Bank Clerk , Bank PO

49 25360
Q:

A jar was full with honey. A person  used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated  the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar  solution. The initial amount of honey in the jar was filled with the sugar solution. The initial amount of honey in the jar was:

A) 1.25 kg B) 1 kg
C) 1.5 kg D) None of these
 
Answer & Explanation Answer: A) 1.25 kg

Explanation:

Let the initial amount of honey in the jar was K, then 

 512=K1-154    ∵ 20% =20100=15

        or      

512=K454

Therefore, K = 1250

Hence initially the honey in the jar= 1.25 kg

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32 24943
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 =  3-3x8+xlitres.

 

Quantity of syrup in new mixture =  5-5x8 litres.

 

  3-3x8+x=5-5x8

 

=>   5x + 24 = 40 - 5x 

 

=>   10x = 16    => x = 8/5

 

So, part of the mixture replaced = 85×18 = 1/5.

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159 24742
Q:

In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 liters of pure milk , the percentage of milk in the mixture  become 76%. The quantity of mixture is:

A) 65 liters B) 91 liters
C) 38 liters D) None of these
 
Answer & Explanation Answer: B) 91 liters

Explanation:

         Milk             Water 

         74%             26%        (initially) 

         76%             24%        ( after replacement) 

 

  Left amount = Initial amount 1-replaced amounttotal amount 

   24  = 261-7k

=> k = 91 

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52 24310