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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)

Comments(7)

Sai Ram Sagar

2015-10-16 05:55:26

Proof of rule of alligation is very helpful. From that we can derive for many

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)

20

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

00

amol palekar

2015-02-03 13:00:38

mean value means the value that u want to make after mixing two elements