## Averages, Ratio and Proportion

Theory

"Averages, Percentages and Ratio and Proportion" is one of the easiest topics in quantitative section in CAT. The theory involved in this section is just an extension of high school mathematics. It is for this reason that questions from these topics are often asked in conjunction with other topics. The fundamentals of this topic are hence important not just from a stand-alone perspective, but also to answer questions from other topics.

Formula
• The average of n terms equals $$\frac{x_1+x_2+. . .+x_n}{n}$$
Formula
• The weighted average of n terms equals $$\frac{w_1*x_1+ w_2*x_2+. . .+ w_n*x_n}{ w_1+ w_2+ . . . w_n}$$
Formula
• Percentage Change = (Final Value – Initial  Value)/Initial Value * 100
Formula
• For two successive changes of of x% and y%, the total % change is (x + y + xy/100)%
Theory
• Alligation Rule: This is used to find the ratio of individual components in a mixture. If two components A and B, costing Rs. X and Rs. Y individually, are mixed and the resultant mixture has an average price of Rs. Z, then the ratio of A and B in the mixture is $$\frac{Z-Y}{X-Z}$$
Formula
• If a, b, c, d and x are positive integers such that $$\frac{a}{b}=\frac{c}{d}$$

1. If $$a < b$$, $$\frac{a+x}{b+x} > \frac{a}{b}$$
2. If $$a > b$$, $$\frac{a+x}{b+x} < \frac{a}{b}$$
3. $$\frac{a+c}{b+d}=\frac{a}{b}=\frac{c}{d}$$
4. $$\frac{a+b}{a-b}=\frac{c+d}{c-d}$$
Formula

In N liters mixture of a solution C, if the amount of liquid A is 'a' liters then the concentration of A in the solution is a*100/N %