Averages, Ratio and Proportion

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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 Questions
  • The average of n terms equals $$\frac{x_1+x_2+. . .+x_n}{n}$$
Formula Questions
  • 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 Questions
  • Percentage Change = (Final Value – Initial  Value)/Initial Value * 100
  • x % of T = $$\dfrac{x}{100}\times\ T$$
Formula Questions
  • For two successive changes of of x% and y%, the total % change is (x + y + xy/100)%
Formula Questions
  • 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. If $$a > b$$, then $$\frac{a-x}{b-x} > \frac{a}{b}$$
    4. If $$a < b$$, then $$\frac{a-x}{b-x} < \frac{a}{b}$$
    5. $$\frac{a+c}{b+d}=\frac{a}{b}=\frac{c}{d}$$
    6. $$\frac{a+b}{a-b}=\frac{c+d}{c-d}$$
Formula Questions

If x is directly proportional to y => x = ky

If x is directly proportional to square of y => x = $$ky^2$$

If x is directly proportional to cube of y => x = $$ky^3$$

Here, 'k' is a proportionality constant.

When x is indirectly proportional to y => $$x=\dfrac{k}{y}$$

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