In this post, we will be learning about mixture and alligation questions and answers. We will see many mixture and alligation questions and answers with tricks/shortcut etc. Have you ever been in a situation where you need to find the price of a mixture containing component A and B at given price ? We will solve such questions in this post. We will also see rule of alligation used to solve such questions. Alligation and Mixture are very important topic in quantitative aptitude for competitive exams like IBSP, SSC, Railways exams etc.

So, let start the learning now.

Getting Started

This post contains three sections –

• Section A – This section contains important formulas, short tricks, concepts on Mixture and alligation.
• Section B – This section contains some examples that demonstrates how to solve questions on alligation and mixture using short tricks, formulas shown in section A.
• Section C – Go to this section to solve some problems on mixture and alligation.

Now,

Where to start from?

We recommend go through section A, then section B, then section C. Even if you are familiar with this topic, do not just skip section A and section B.

Section A: (Terms & Formulas)

Now, we will go through some formaulas, concepts used in Mixture and Alligation –

Alligation : A rule that makes us find the ratio in which 2 or more ingredients at the given price are mixed to produce a mixture at a given price.

Mixture : A mix of 2 or more ingredients forms a mixture.

Mean Price – The price of an unit quantity of mixture is Mean price.

Formulae – If two ingredients A and B respectively are mixed in some proportion with A being the cheaper component and B being the dearer (costlier) component, then the rule of alligation says:

(Quantity of Cheaper / Quantity of dearer) = ((C.P of dearer) – (Mean Price)) / ((Mean price) – (C.P of cheaper))

Where ,

C.P of dearer means the cost price of the costlier component (d)

C.P of cheaper means the cost price of the cheaper component (c)

(Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c)

Till now, we have seen some important terms, concepts that will be used in mixture and alligation questions and answers.

Note – In our examples, we have converted rupees into paise to make calculation easier (Re. 1 = 100 Paise).

Section B: (Examples)

Now, we will see how to approach any questions on mixture and alligation. What are the key factors we should look into before trying to solve such questions. Please do not move to next section without going through each mixture and alligation questions and answers.

Example 1

Find the ratio in which coffee at Rs. 62 per kg must be mixed with chicory at Rs. 72 per kg so that the mixture must be worth Rs. 64.50 per kg?

Solution: 

As per the rule of alligation,

Hence, (Coffee : Chicory) = 750 : 250 = 3 : 1

Example 2

Find the ratio in which water must be mixed with Juice concentrate to gain 20% by selling the mixture at cost price?

Solution:

Let cost price of juice concentrate be = Rs 1 per litre
Then, Selling price of 1 ltr of the mixture = Rs 1
Gain obtained = 20%
Hence, C.P. of 1 ltr of mix = (100 / 120) x 1 = Rs. 5 / 6

By the rule of alligation, we have:

Hence, Ratio of water and juice concentrate = 1 / 6 : 5 / 6  = 1 : 5

Example 3

A sum of Rs. 9500 is lent out partly at 11% and partly at 15% simple interest. His total income after 1 ½ years was Rs. 1800. Find the sum lent at different rates.

Solution:

Total Interest on Rs 9500 for 1 ½  yrs = Rs. 1800
Rate = [100 * 1800] / [9500 * (3 / 2)] % = 12.6%

By the rule of alligation, we have:

Hence, 1^st part : 2^nd part = 2.4 : 1.6  = 3 : 2

Hence, First part = Rs [9500 * (3 / 5)] = Rs. 5700

Second part = 9500 – 5700 = Rs. 3800

Till now, we have seen how to attempt mixture and alligation questions and answers.

NOTE – Please try to solve question by yourself first. Then check solution by clicking on Show Answer button.

Section C (Exercises)

In this section, we will see different mixture and alligation questions and answers (with short tricks, if available).

Mark against the correct answer:

Question 1

Find the ratio in which brand A rice at Rs. 9.30 per kg must be mixed with local brand B rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg?

(a) 7 : 8
(b) 8 : 7
(c) 31 : 36
(d) 38 : 31

Question 2

Find the ratio in which Sugar of brand A at Rs. 3.2 per kg be mixed with Sugar brand B at Rs. 2.90 per kg so that the mixture be worth Rs. 3.08 per kg?
(a) 4 : 3
(b) 3 : 4
(c) 2 : 3
(d) 3 : 2

Question 3

How many kg’s of Chilli powder costing Rs. 9 per kg must be mixed with 27 kg of Coriander powder costing Rs. 7 per kg so that there will be a gain of 10% on selling the full mixture at Rs. 9.24 per kg.
(a) 54 kg
(b) 63 kg
(c) 36 kg
(d) 42 kg

Question 4

In what ratio must water be mixed with cement to gain 50/3 % on selling the mixture at cost price?
(a) 2 : 3
(b) 4 : 3
(c) 6 : 1
(d) 1 : 6

Question 5

Water and milk are mixed in two containers in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture worth Rs. 8 per litre?

(a) 2 : 7

(b) 5 : 2

(c) 3 : 5

(d) 5 : 7

Question 6

In what ratio must water be mixed with a chemical solution costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre?

(a) 3 : 2

(b) 2 : 3

(c) 1 : 2

(d) 2 : 1

Question 7

A sum of Rs. 4500 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the amount of annual interest is Rs. 352, the sum lent at 8% is:

(a) Rs. 4600

(b) Rs. 4125

(c) Rs. 4800

(d) Rs. 2800

Question 8

A Shopkeeper has 1000 kg of wheat, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity of wheat sold at 18% profit is:

(a) 640 kg

(b) 560 Kg

(c) 600 kg

(d) 400 kg

Question 9

Two containers contain milk and water mixed in the ratio 4:3 and 2:3. Find the ratio in which these mixtures must be mixed to form a new mixture containing half milk and half water?

(a) 7:5

(b) 1:2

(c) 2:1

(d) 6:5

Question 10

A tin full of Juice contains 40% soda. A part of this juice is replaced by another containing 19% soda and the now the percentage of soda was found to be 26%. The quantity of bear replaced is:

(a) 1 / 3

(b) 2 / 3

(c) 2 / 5

(d) 3 / 5

Question 11

729 ml of mixture contains paint and water in the ratio 7 : 2. How much water needs to be added to get a new mixture containing paint and water in the ratio 7 : 3 ?

(a) 79 ml

(b) 81 ml

(c) 72 ml

(d) 91 ml

Question 12

A sum of money Rs. 312 was divided among 100 students in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls are

(a) 40

(b) 60

(c) 35

(d) 65

Question 13

Raja covered distance of 2000 km in 18 hours partially by car at 72 kmph and partly by express train at 160 kmph.  The distance covered by bus is:

(a) 1280 km

(b) 720 km

(c) 860 km

(d) 640 km

Question 14

A total sum of Rs. 36.90 is made up of 180 coins with 10 paisa and 25 paisa coins. The number of 10 paisa coins is:

(a)126

(b) 54

(c) 120

(d) 60

Question 15

A shopkeeper sells milk at cost price but he mixes it with water and thereby gains 10%. The percentage of water in the mixture is:

(a) 25%

(b) 20%

(c) 6 ¼%

(d) 9.09%

Question 16

A mixture of 20 kg of alcohol and water contains 10% water. To raise the percentage of water to 25%, How much water needs to be added to the mixture?

(a) 4 kg

(b) 5 kg

(c) 8 kg

(d) 30 kg

Question 17

A container contains 50 kg of raw rice. From this container 5 kg of raw rice was taken out and replaced by basmathi rice. This process was repeated further two times. How much raw rice is now contained by the container?

(a) 37.36 kg

(b) 36.45 kg

(c) 36 kg

(d) 35.34 kg

Question 18

A Container can contain a mixture of two liquids Y and Z in the ratio of 7:5. When 9 litres of mixture are drawn off and the can be adjusted to be filled with Z, the ratio of Y and Z becomes 7:9. How many litres of liquid Y were contained by the container initially?

(a) 25

(b) 21

(c) 20

(d) 10

Question 19

How many kgs of wheat costing Rs. 9.00 per kg must be mixed with 36 kgs of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?

(a) 8.8 kg

(b) 7.2 kg

(c) 7.5 kg

(d) 9.5 kg

Question 20

A sum of Rs. 118 was split up among 50 students in such a way that each boy received Rs. 2.60 and each girl received Rs. 1.40. Find, how many boys and girls are there in the class?

(a) Boys – 35, Girls – 15

(b) Boys – 25, Girls – 25

(c) Boys – 10, Girls – 40

(d) Boys –  40, Girls – 10

Question 21

Hema travelled a distance of 80 kms in 8 hrs, partly on foot at 8 kmph and partly by scooter at 17 kmph. Find the distance travelled on foot. (kmph = Kilometer per hour)

(a) 56 km

(b) 46 km

(c) 50 km

(d) 40 km

Question 22

Two containers contain alcohol and water combined in the ratio 5 : 2 and 7 : 6 respectively. In which ratio these must be mixed to obtain a new mixture in container 3 containing alcohol and water in the ratio 8 : 5

(a) 7 : 9

(b) 8 : 9

(c) 3 : 2

(d) 9 : 7

Question 23

A mixture of 40 kg. of rice and dhall contains 20% rice. To raise the percentage of dhall to 25%, How much rice needs to be added to the mixture?

(a) 4.5 kg.

(b) 2.6 kg.

(c) 3.5 kg.

(d) 2.8 kg.

Thus, we went through different concepts, short tricks, terms to solve mixture and alligation questions and answers.

That’s end of topic on mixture and alligation questions and answers.