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CAT Quantitative Aptitude: Proportions & Variations

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Sep 1, 2014 16:50 IST
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Proportion:

Proportion is the equality of two fractions, that is a : b = c : d. This can be represented as a : b :: c : d,

Where a and d are called extremes and b and c are called the mean of the ratio.

Fourth, Third and mean proportions:

                                                           In a : b :: c : d,

d is the fourth proportion of a, b and c

and c is the third proportion of a and b.

The mean proportion of a and b is √ab

Invertendo:

If a : b = c : d then

                                         b : a :: d : c or b/a = d/c

Alterando:

If a : b= c : d then

                                         a : c :: b : d or   a/c = b/d

Componendo:

If a : b = c : d then

                                          (a + b)/b = (c + d)/d

Dividendo:

If a : b = c : d then

                                           (a - b)/b = (c - d)/d

Componendo & Dividendo:

If a : b = c : d then

                                            (a + b)/(a - b) = (c + d)/(c - d)

Properties of proportion:

Product of extremes is equal to the product of means

If a : b :: c : d, then

                                                ad = bc

If three quantities are in proportion as in a : b :: b: c, then,

                                                ac = b2

Where b is the mean proportion to a and b

C is the third proportion to a and b

    • If three quantities are in proportion as in a : b :: b : c, then,

                                                a ∶ c =  a2 : b2

Variation:

Direct variation: If two quantities a and b vary directly that is if a increases then b also increases and vice versa, and if there is a non-zero constant m, then,

                                                a = mb

Their relation is denoted as a ∝ b

Inverse variation: If two quantities a and b vary inversely that is if a increases then b decreases and vice versa, and if there is a non-zero constant m, then,

a = m/b

Their relation is denoted as a ∝ 1/b

Learn more on Ratios & its properties:

Properties of Ratios: Part 1

Properties of Ratios: Part 2

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