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 Example 1
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 shopkeepar mix two type rice worth Rs.50 a kg and Rs.58 a kg so that by selling the mixture at Rs. 58.30 a kg and he may gain 10% ?
Answer : Selling price of 1 kg rice of the mixture = Rs.58.30, Gain = 10%.
Cost price of 1kg of the mixture = Rs. 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.

Required Ratio of both materials is 5 : 3.

 

 

Example 2:
In what proportion sugar at 3.25 per kg be mixed with sugar at Rs 3.80 per kg, So that the mixture be worth Rs 3.50 a kg ?
Answer:
Formula applied :
Quantity of cheaper / Quantity of dearer = CP of dearer – Mean price / Mean price – CP of cheaper
= 380 – 350 / 350 – 325
Quantity of cheaper rice / Quantity of dearer rice = 30 / 25 = 6 / 5
So, They must be mixed in the ratio 6 : 5.

 

 

Example 3:
In a What ratio Wheat at Rs. 12.30 per kg be mixed with wheat 18.30 per kg, so that the mixture be worth Rs.15 per kg?
Answer :
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.

Required Ratio of both materials is 11 : 9.

 

 

Example 4: In a mixture of water and milk with 18 litres of water worth 96 paise per liter. If milk be worth Rs.1.12 per litre. Find how much milk is present in that mixture ?
Answer : 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 litres.

 

 

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

Answer :

 

 

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 its gain is 20 % and that mixture is selling at the price of Rs. 8.40 per kg ?
Answer : Selling price of 1 kg of mixture = Rs.8.40, on this gain = 20%.
So, cost price of 1 kg of mixture = Rs.100 x 8.40 / 120 = Rs.7.00.
using alligation rule

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

 

 

Example 7:
In a goldsmith has two qualities of gold one of 14 carats and another of 17 carats purity. In what propotion should he mix both to make an ornament of 16 carats purity ?
Answer :
Formula applied :
Quantity of cheaper / Quantity of dearer = CP of dearer – Mean price / Mean price – CP of cheaper
= 17 – 16 / 16 – 14 = 1 / 2
Quantity of cheaper rice / Quantity of dearer rice = 17 – 16 / 16 – 14 = 1 / 2
So, They must be mixed in the ratio 1 : 2.

 

 

Example 8: A grocery has 600 kg of rice, In part of which he sells at 12% profit and the rest of at 24% profit, and he gains 16% on the entire. Find quantity sold at 24% profit.
Answer :

By the rule of alligation :
profit on First part = ( profit on First part ) = 12%
profit on second part = ( profit on second part ) = 24%
profit on Mean = ( 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, Ratio of 1st and second parts = 8 : 4 = 2 : 1.
quantity sold of second part = (1 x 600 / 3) = 200 kg.

 

Example 9:
Find the ratio in which fresh sugar at Rs. 8.40 a kg be mixed with sugar at Rs. 4.80 a kg to produce a mixture worth Rs. 6.80 a kg.
Answer : Using rule of alligation:

required ratio = 200 : 160 = 5 : 4

 

 

Example 10: Find what ratio must a grocer mix two type of tea price Rs. 20 and Rs. 22 per kg, So as to get a mixture worth
Rs. 18.50 kg?
Answer :
using the rule of alligation:

Required rate = 350 : 150 = 35 : 15 = 7 : 3.

 

 

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

Let Cost Price of 1 litre milk isRs. 1.
So, Selling Price of 1 litre of mixture is Rs. 1, and he Gain = 20%.
Cost Price of 1 litre mixture is = Rs. 100 x 1 / 120 = 5 / 6.

using alligation rule :

Ratio of milk to water = 5 / 6 : 1 / 6 = 5 : 1.

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

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.
Answer :
Let the C.P. of milk be Rs. 1 per litres.
milk in 1 litre mixture of vessels P = 5 / 7 litre,
C.P. of 1 litre mixture in vessels P = Rs 5 / 7.

milk in 1 litre mixture of vessels Q = 7 / 13 litre.
C.P. of 1 litre mixture in vessels Q = Rs. 7 / 13.

milk in 1 litre mixture of R = 8 / 13 litre.
Mean price = Rs. 8 / 13.

Using alligation rule :

So, the required ratio = 1 / 13 : 9 / 91 = 7 : 9.

 

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