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Alligation & Mixtures MCQ

What is a mixture?
A mixture is a combination of two or more substances in a specific proportion.
What is alligation?
Alligation is a rule that helps calculate the proportion and strength of each substance in a mixture.
How is alligation used?
Alligation is used to find the ratio in which ingredients should be mixed to produce a mixture with a desired price. It can also be used to find the quantity of a mixture given the quantities of its ingredients.

Types of alligation
There are two types of alligation: alligation medial and alligation alternate. Alligation medial is used to find the quantity of a mixture, while alligation alternate is used to find the amount of each ingredient needed to make a mixture.

Mixture: It is the process of mixing two or more elements/ingredients together.

Allegation: It is a process or a rule that tells us how to mix two or more ingredients/mixtures to get the desired mixture of a certain price & concentration.

Now there are 2 ways of applying the allegation technique to questions.
Formula Method:

Quantity of cheaper/ Quantity of dearer = (Price of dearer – Mean price)/ (Mean Price- Price of cheaper)
Diagram Method:

The above-mentioned formula can be better understood using the diagram method & it is more convenient to use this method.

MCQ Questions on Alligation & Mixtures

1. The ratio in which a man must mix rice at Rs.10.20 per kg and Rs.14.40 per kg to make a mixture worth Rs.12.60 per kg, is

a) 18 : 24         b) 3 : 4             c) 2 : 5             d) 4 : 3

Answer: (b)
Required ratio = 1.8 : 2.4
= 18 : 24 = 3 : 4

2. The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is

a) 60 litres                  b) 96 litres      c) 40 litres      d) 35 litres

Answer: (c)
Let the quantity of milk in the mixture = 7x litres and that of water = 5x litres.
According to the question,
7x / 5x+15 = 7/8
56x = 35x + 105
56 x – 35 x = 105
21x = 105
X = 105/21 = 5
Required quantity of water
= (5x + 15) litres
= 5 × 5 + 15 = 40 litres

3. Zinc and copper are in the ratio of 5 : 3 in 200 gm of an alloy. How many grams of copper be added to make the ratio as 3 : 5?

a) 72                b) 66                c) 1 / 200                     d) 133  1/3

Answer: (d)
Weight of zinc = 200 × (5/8) = 125 gram
Weight of copper = 200× (3/8) = 75 gram.
Let the ratio of 125 gram zinc and x gram copper be 3 : 5
= 125/ x = 3 / 5
x= (125×5) / 3
= 625/3 gram
Addition of copper in mixture
= (625/3) −75= ( 625−225 ) / 3
= 400 / 3 =133 1/3 gram

4. A mixture of 30 litres contains milk and water in the ratio of 7 : 3. How much water should be added to it so that the ratio of milk and water becomes 3 : 7 ?

a) 56 litres                  b) 63 litres                  c) 49 litres                  d) 40 litres

Answer: (d)
Quantity of milk in 30 litre mixture
= ( 30/10) ×7 = 21litres
Quantity of water = (30/10) ×3=9 litres
Suppose x litres more water is added.
According to question,
21/(9+x) = 3/7
9 + x = 49
x = 40 litres

5. In 30 litres mixture of acid, the ratio of acid and water is 2 : 3 . What amount of water should be added to the mixture so that the ratio of acid and water becomes 2 : 5 ?

a) 18 litres                  b) 12 litres                  c) 15 litres                  d) 10 litres

Answer: (b)
In 30 litres of mixture,
Acid = (2/5) ×30 = 12 litres
Water = (3/5) ×100 = 18 litres
12/(18+x) = 2/5
60 = 36 + 2x
2x = 60 – 36 = 24
x = 12 litres of water.