# 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 vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained ?

 A) 5:3 B) 1:4 C) 4:1 D) 9:1

Explanation:

Milk = 3/5 x 20 = 12 liters, water = 8 liters

If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.

Remaining milk = 12 - 6 = 6 liters

Remaining water = 8 - 4 = 4 liters

10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

The ratio of milk and water in the new mixture = 16:4 = 4:1

If the process is repeated one more time and 10 liters of the mixture are removed,
then amount of milk removed = 4/5 x 10 = 8 liters.

Amount of water removed = 2 liters.

Remaining milk = (16 - 8) = 8 liters.

Remaining water = (4 -2) = 2 liters.

Now 10 lts milk is added => total milk = 18 lts

The required ratio of milk and water in the final mixture obtained

= (8 + 10):2 = 18:2 = 9:1.

34 21391
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

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

61 21341
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.

33 19364
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

43 19007
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

44 18270
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

Explanation:

Milk             Water

74%             26%        (initially)

76%             24%        ( after replacement)

Left amount = Initial amount

24  = 26$1-7k$

=> k = 91

36 16696
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

16617
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%.