1. Alligation:
It is the rule that 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 desired price.
2. Mean Price:
The cost price of a unit quantity of the mixture is called the mean price.
3. Rule of Alligation:
If two ingredients are mixed, then
(Quantity of cheaper) = (C.P. of dearer) - (Mean price)
(Quantity of dearer) (Mean price) - (C.P. of cheaper)
We present as under:
C.P. of a unit quantity of cheaper C.P. of a unit quantity of dearer
(c) (d)
(m)
(d-m) (m-c)
(Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).
4. Suppose a container contains x units of liquid from which y units are taken out and replaced by
water.
After n operations the quantity of pure liquid = [ x(1-y/x)^n]units.