# 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 = $x{\left(1-\frac{y}{x}\right)}^{n}$ units.

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

Explanation:

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

$512=K1-154$

or

$512=K454$

Therefore, K = 1250

Hence initially the honey in the jar= 1.25 kg

32 27077
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%

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%.

40 26884
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

Explanation:

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

27             :                13

72 26416
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 ?

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

25758
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

Explanation:

2 : 3                   4 : 5                    5 : 7

= 72/180

= 80/180

= 75/180

=>     5   :   3

Therefore, the ratio is  5: 3

50 25705
Q:

From  a container of wine, a thief has stolen 15 liters of wine and replaced it with same quantity of water.He again repeated the same process. Thus in three attempts the ratio of wine and water became 343:169. The  initial amount of wine in the container was:

 A) 75 liters B) 100 liters C) 150 liters D) 120 liters

Explanation:

It means

Thus ,

$343x=512x1-15K3$

$⇒343512=783=1-15k3$

=> K = 120

Thus the initial amount of wine was 120 liters.

40 25421
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

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 =  $3-3x8+x$litres.

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.

160 24369
Q:

In the 75 litres of mixture of milk and water, the ratio of milk and water is 4:1. The quantity of water required to make the ratio of milk and water 3:1 is

 A) 1 litre B) 3 litres C) 4 litres D) 5 litres

Explanation:

Total quantity of mixture = 75 litre

Milk  :  Water  =  4  :  1

3       :       1