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Important Formulas - Mixture and Alligation

1. Alligation

Alligation is the rule which 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 specified price.

2. Mean Price

Mean price is the cost price of a unit quantity of the mixture

3. Suppose a container contains $x$ units of a liquid from which $y$ units are taken out and replaced by water. After $n$ operations, quantity of pure liquid
$=x\left(1-\dfrac{y}{x}\right)^n$ units.
4. Rule of Alligation

If two ingredients are mixed, then
$\left(\dfrac{\text{Quantity of cheaper}}{\text{Quantity of dearer}}\right) $ $= \left(\dfrac{\text{CP of dearer - Mean Price}}{\text{Mean price - CP of cheaper}}\right)$

The above formula can be represented with the help of the following diagram which is easier to understand.

Rule of Alligation

=> (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c)

Comments(7)

profileSai Ram Sagar
2015-10-16 05:55:26 
Proof of rule of alligation is very helpful. From that we can derive for many
like 1 dislike 0 reply
profilelikender
2015-09-09 18:47:26 
can you plz give some proof of this formulae............
like 1 dislike 0 reply
profileRaj
2015-09-09 20:10:25 
Proof of Rule of Alligation formula

Let cost price of unit quantity of cheaper ingredient = c
cost price of unit quantity of dearer ingredient = d

Suppose 'a' units of cheaper ingredient and 'b' units of dearer ingredient are mixed.

Total quantity of the mixture = a + b
Total cost price of the mixture = (ac + bd)

cost price of unit quantity of the mixture (mean price) = $\dfrac{\text{ac + bd}}{\text{a+b}}$

Suppose mean price = m
=> $\dfrac{\text{ac + bd}}{\text{a+b}}$ = m
=> am + bm = ac + bd
=> am - ac = bd - bm
=> a(m - c) = b(d -m)
=> a/b = (d -m)/(m - c)
=> a : b = (d -m):(m - c)
like 2 dislike 0
profileappu
2016-03-18 01:22:02 
proof is excellent. I went through a lot of websites, none of them had given any proof. proof makes the idea clear. So thank you very much
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profileamol palekar
2015-02-03 13:00:38 
mean value means the value that u want to make after mixing two elements
like 0 dislike 0 reply
profileAnna
2014-11-10 08:50:03 
I suggest that each rule or formula should have an example to make it more understandable.

Variables such as x and y makes the explanation more complicated
like 0 dislike 0 reply
profilePRAN KUMAR
2013-04-23 20:05:01 
I am preparing for DVC. And i think these formula are very helpful to crack it.
Thanking you.
like 0 dislike 0 reply

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