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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. => (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) Sai Ram Sagar
2015-10-16 05:55:26
Proof of rule of alligation is very helpful. From that we can derive for many 1 0 reply likender
2015-09-09 18:47:26
can you plz give some proof of this formulae............ 1 0 reply Raj
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) 2 0 appu
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 0 0 amol palekar
2015-02-03 13:00:38
mean value means the value that u want to make after mixing two elements 0 0 reply Anna
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 0 0 reply PRAN 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. 0 0 reply