short tricks for ratio nd proprtion

Hi Ritu,

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 $$\frac{Z-Y}{X-Z}$$

If a, b, c, d and x are positive integers such that $$\frac{a}{b}=\frac{c}{d}$$

If $$a < b$$, $$ \frac{a+x}{b+x} < \frac{a}{b}$$
If $$a > b$$, $$ \frac{a+x}{b+x} > \frac{a}{b}$$
$$\frac{a+c}{b+d}=\frac{a}{b}=\frac{c}{d}$$
$$\frac{a+b}{a-b}=\frac{c+d}{c-d}$$

You can find more shortcuts, tips and tricks at the following link:

https://cracku.in/cat/quantitative-aptitude/avgs-ratio-proportion/cheatsheet