##
*Mixture* and Alligation *Shortcut* Methods

**Formulae:**

1. Average = sum of quantities/number of quantities

2. Sum = avg * no. of quantities

3. If the numbers are in A.P. (Arithmetic Progression), then the avg of numbers is given by

Avg = sum/n =[ (n/2)(a+l)]/n

= (a+l)/2

Where n – no. of quantities

a – first term or value

l – last term or value

4. Weighted Average:

Section1:

No. of quantities: m

Avg of section1: p

Section2:

No. of quantities: n

Avg of section1: q

Avg of section1 and section2 = (m*p + n*q)/(m +n)

**Points to remember/Shortcuts**

1. Average lies between minimum and maximum values.

a. Avg > minimum value

b. Avg < maximum value

2. If every quantity is increased/decreased by ‘k’ value, then the avg also get increased/decreased by the same ‘k’ value.