# 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:

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

 A) 1:3 B) 2:3 C) 3:4 D) 4:5

Explanation:

By the rule of alligation:
Cost of 1 kg rice of 1st kind                  Cost of 1 kg rice of 2nd kind

Required ratio = 60 : 90 = 2 : 3

66 33701
Q:

The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:

 A) 25 B) 30 C) 45 D) cannot be determined

Explanation:

pool : kerosene

3  :  2(initially)

2  :  3(after replacement)

(for petrol)   $23=1-10k$

=> K = 30

Therefore the total quantity of the mixture in the container is 30 liters.

83 31479
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.

53 31273
Q:

A container contains 50 litres of milk. From that 8 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container ?

 A) 24.52 litres B) 29.63 litres C) 28.21 litres D) 25.14 litres

Explanation:

Given that container has 50 litres of milk.

After replacing 8 litres of milk with water for three times, milk contained in the container is:

$⇒501-8503$

$⇒50×4250×4250×4250$  = 29.63 litres.

49 30994
Q:

The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be  formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?

 A) 4 B) 5 C) 8 D) None of these

Explanation:

Wine                         Water

8L                              32L

1                :               4

20 %                           80% (original ratio)

30 %                           70% (required ratio)

In  ths case, the percentage of water being reduced when the mixture is being replaced with wine.

so the ratio of left quantity to the initial quantity is 7:8

Therefore , $78=1-K40$

=> K = 5 Lit

92 29938
Q:

The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?

 A) 25 B) 21 C) 12 D) 24

Explanation:

Therefore x = 21%

138 29708
Q:

From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of mixture is:

 A) 15 B) 16 C) 25 D) 31

Explanation:

Let quantity of mixture be x liters.

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, Where n = no of operations .

So, Quantity of Milk = $x1-6x2$

Given that, Milk : Water = 9 : 16

=> Milk : (Milk + Water) = 9 : (9+16)

=> Milk : Mixture = 9 : 25

Therefore, $x1-6x2x=925$

=> x = 15 liters

65 29209
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