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# Mixture and Alligation Example 1

Mixture and Alligation shortcut tricks are very important thing to know for your exams. Time takes a huge part in competitive exams. If you know time management then everything will be easier for you. Most of us skip that part. Here in this page we give few examples on Mixture and Alligation shortcut tricks. All tricks on mixture and alligation are provided here. Visitors please read carefully all shortcut examples. These examples will help you to understand shortcut tricks on Mixture and Alligation.

Before doing anything we recommend you to do a math practice set. Write down twenty math problems related to this topic on a page. Do first ten maths using basic formula of this math topic. You also need to keep track of timing. After finish write down total time taken by you to solve those ten maths. Now read our examples on mixture and alligation shortcut tricks and practice few questions. After doing this go back to the remaining ten questions and solve those using shortcut methods. Again keep track of Timing. You will surely see the improvement in your timing this time. But this is not all you need. If you need to improve your timing more then you need to practice more.

Math section in a competitive exam is the most important part of the exam. It doesn’t mean that other topics are not so important. But if you need a good score in exam then you have to score good in maths. Only practice and practice can give you a good score. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that without using shortcut tricks you can’t do any math problems. You may have that potential that you may do maths within time without using any shortcut tricks. But other peoples may not do the same. For those we prepared this mixture and alligation shortcut tricks. We try our level best to put together all types of shortcut methods here. But we may miss few of them. If you know anything else rather than this please do share with us. Your help will help others.

Mixture and Alligation Examples
Here in this Mixture and Alligation Methods and some important formula which need to understand through examples that’s are given in exams. we provide u some example 1 based on mixture and alligation. This is the basic theory of Mixture and Alligation which is applied in question to obtain answers here Mixture and Alligation Methods of example in different form of examples.

In maths exam papers there are two or three question are given from this chapter. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below  given some more example for your better practice.

Example #1
In what ratio must a shopkeeper mix two type of rice worth Rs.50/- per kg and Rs.58/- per kg so that by selling the mixture at Rs.58.30/- per kg and he may gain 10% ?

1. 3 : 2
2. 5 : 2
3. 4 : 3
4. 5 : 3

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How to Solve
Selling price of 1 kg rice of the mixture = Rs.58.30/-.
Gain = 10%.

Cost price of 1 kg of the mixture = 100 x 58.30 / 110
= Rs.53/-.

By the rule of alligation:
C.P.M.1 = ( Cost price of First rice ) = Rs.50/-
C.P.M.2 = ( Cost price of Second rice ) = Rs.58/-
M.P. = ( Mean price of both Material ) = Rs.53.00/-

So,
( C.P.M.1 – M.P. ) : ( C.P.M.2 – M.P.)
= ( 50 – 53 ) : ( 58 – 53 )
= 5 : 3.

So, the required ratio of both materials is 5 : 3.

Rough Workspace

Example #2
In what proportion some sugar of Rs.3.25/- per kg be mixed with another type of sugar of Rs.3.80/- per kg, so that the mixture would be the worth of Rs.3.50/- per kg?

1. 5 : 6
2. 6 : 5
3. 7 : 8
4. 8 : 9

Show Answer Show How to Solve Open Rough Workspace

How to Solve
By the rule of alligation:
Quantity of cheaper / Quantity of dearer = CP of dearer – Mean price / Mean price – CP of cheaper
Quantity of cheaper / Quantity of dearer = 380 – 350 / 350 – 325
Quantity of cheaper / Quantity of dearer = 30 / 25 = 6 / 5

So, They must be mixed in the ratio of 6 : 5.

Rough Workspace

Example #3
In a what ratio wheat of Rs.12.30/- per kg be mixed with wheat of Rs.18.30/- per kg, so that the mixture would be worth of Rs.15/- per kg?

1. 9 : 10
2. 10 : 9
3. 9 : 11
4. 11 : 9

Show Answer Show How to Solve Open Rough Workspace

How to Solve
Here we apply alligation rule that is
( Cheaper quantity ) : ( Dearer quantity ) = ( d – m ) : ( m – c ).

C.P.M.1 = ( Cost price of First material ) = 12.30 = 1230
C.P.M.2 = ( Cost price of Second material ) = 18.30 = 1830
M.P = ( Mean price of both Material ) = 1500

So, ( C.P.M.1 – M.P ) : ( C.P.M.2 – M.P)
= ( 1500 – 1230 ) : ( 1500 – 1830 )
= 270 : 330
= 11 : 9.

So, the required ratio of both materials is 11 : 9.

Rough Workspace

Example #4
In a mixture of water and milk there was 18 liters of water of 96 paise per liter. If the price of the milk be Rs.1.12 per liter. Find how much milk is present in that mixture?

1. 100 Liters
2. 108 Liters
3. 118 Liters
4. 126 Liters

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How to Solve
The mean value is 96 paise and price of water is 0 paise. Using alligation rule the ratio of milk and water is 6 : 1.
So, the quantity of milk is present in this mixture is,
( 6 x 18 )
= 108 liters.
Rough Workspace

Example #5
In what ratio must water be mixed with milk that would worth Rs.18/- per liter to obtain a mixture worth Rs.12/- per liter?

1. 1 : 2
2. 2 : 3
3. 3 : 4
4. 4 : 5

Show Answer Show How to Solve Open Rough Workspace

How to Solve Ratio of water and milk is
6 : 12
= 1 : 2.
Rough Workspace

Example #6
In how many kilogram of tea worth Rs.9/- per kg mixed with 36 kg of tea worth Rs.6/- per kg, so that it’s gain is 20% and that mixture is selling at the price of Rs.8.40/- per kg?

1. 14 kg
2. 16 kg
3. 18 kg
4. 20 kg

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How to Solve
Selling price of 1 kg of mixture = Rs.8.40.
Gain = 20%.

So, cost price of 1 kg of mixture
= 100 x 8.40 / 120
= Rs.7/-.

Using alligation rule Ratio of quantities of 1st and 2nd = 1 : 2
So, 1 : 2 = X : 36
X = 36 x 1 / 2
X = 18 kg.

Rough Workspace

Example #7
A goldsmith has two qualities of gold one of 14 carats and another of 17 carats purity. In what proportion should he mix both to make an ornament of 16 carats purity?

1. 1 : 2
2. 2 : 1
3. 3 : 2
4. 2 : 3

Show Answer Show How to Solve Open Rough Workspace

How to Solve
By using the formula of alligation
Quantity of cheaper / Quantity of dearer = CP of dearer – Mean price / Mean price – CP of cheaper
= 17 – 16 / 16 – 14
= 1 / 2.

So, They must be mixed in the ratio of 1 : 2.

Rough Workspace

Example #8
A grocery has 600 kg of rice. He sells a part from it at a 12% profit and the rest of at 24% profit. He gains 16% on the entire. Find quantity sold at 24% profit.

1. 175 kg
2. 200 kg
3. 220 kg
4. 245 kg

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How to Solve
By the rule of alligation
Profit on First part = 12%
Profit on second part = 24%
Profit on Mean = 16%
So,
( profit on First part – Profit on Mean ) : ( Profit on Second part – Profit on Mean )
= ( 12% – 16% ) : ( 24% – 16% )
= 8 : 4
= 2 : 1.

So, the ratio of First and Second parts,
= 8 : 4
= 2 : 1.

Quantity sold of second part,
= ( 1 x 600 / 3 )
= 200 kg.

Rough Workspace

Example #9
Find the ratio in which fresh sugar of Rs.8.40/- per kg be mixed with sugar of Rs.4.80/- per kg to produce a mixture worth Rs.6.80/- per kg.

1. 3 : 4
2. 4 : 3
3. 4 : 5
4. 5 : 4

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How to Solve
Using rule of alligation: So, the required ratio is,
= 200 : 160
= 5 : 4.
Rough Workspace

Example #10
Find in what ratio must a grocer mix two type of tea of Rs.20/- and Rs.22/- per kg, so that the mixture would be worth of Rs.18.50/- kg?

1. 3 : 7
2. 7 : 3
3. 5 : 7
4. 7 : 5

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How to Solve
Using the rule of alligation So, the required rate is,
= 350 : 150
= 35 : 15
= 7 : 3.

Rough Workspace

Example #11
A dishonest shopkeeper professes to sell his milk at the cost price. But he mixed it with water and because of that he gains 20%. Find the percentage of water in the mixture is.

1. 12.98%
2. 14.45%
3. 16.67%
4. 18.35%

Show Answer Show How to Solve Open Rough Workspace

How to Solve
Let, Cost price of 1 liter milk is Rs.1/-.
So, sell price of 1 liter of mixture is Rs.1/-, and he Gain = 20%.
Cost Price of 1 liter mixture is,
= 100 x 1 / 120
= 5 / 6.

Using alligation rule: Ratio of milk to water is,
5 / 6 : 1 / 6
= 5 : 1.

So, the percentage of water in the mixture is,
= 1 x 100 / 6
= 16.67%.

Rough Workspace

Example #12
Two vessels P and Q has contain milk and water in the ratio of 5 : 2 and 7 : 6 respectively. What would be the ratio in which these mixture now be mixed and obtain a new mixture in a vessels R contain milk and water in the ratio of 8 : 5 ?

1. 5 : 7
2. 7 : 8
3. 9 : 7
4. 7 : 9

Show Answer Show How to Solve Open Rough Workspace

How to Solve
Let, the Cost price of milk be Rs.1/- per liters.
Milk in 1 liter mixture of vessels P = 5 / 7 liter,
Cost price of 1 liter mixture in vessels P = Rs. 5 / 7.

Milk in 1 liter mixture of vessels Q = 7 / 13 liter.
Cost price of 1 liter mixture in vessels Q = Rs. 7 / 13.

Milk in 1 liter mixture of R = 8 / 13 liter.
Mean price = Rs. 8 / 13.

Using alligation rule: So, the required ratio is,
= 1 / 13 : 9 / 91
= 7 : 9.

Rough Workspace

### Few examples of Mixture and Alligation with Shortcut Tricks

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1. nitish says:

Thank u so much it has really turned things a bit easy way

2. yo man!
this is really best … can easily revise things .. logically formulated and wonderfully explained..

3. Sreehari says:

Well explained. Thank you.

4. triveni says:

Plz explain que no 12

5. jeya says:

thanks well explained

6. Ravikumar says:

Very Very awesome and quite useful sir.

7. Pratyush Maity says:

tnx

8. Vamsi says:

Awesome explanations. Really helpful for quick reference.

• thanks, keep visiting

9. raj kumar singh says:

Thanks its good method for competitive exams

10. Vijayakumar says:

Super

11. Rounak R Kamble says:

Nice explanation…

12. sandip says:

very nice

13. Dinesh bansal says:

Good collection of questions. Explained really well.

14. Shivani tomar says:

Keep posting more tricks

15. Aryakhushi singh says:

nice explanation

16. Abhijit Ray says:

Well explained.

17. kalaiselvi says:

super