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Quantitative Aptitude Course in Chennai by KCS Education

Ratio and proportion

Ratio: Ratio of a and b is the fraction a/b represented as a : b, Here a is called as antecedent and b is called as consequent.

Rule: Multiplication or division of each term in a ratio will not affect the ratio.

Example: 4 : 7 = 8 : 14 = 12 : 21

15 : 20 = 3 : 4

Proportion: The equality of two ratios is called Proportion. If a : b :: c : d means a : b = c : d, we say a, b, c, d are in proportion. Here in the expression, a : b :: c : d, a, d are called extremes and b, c are called mean terms.

Product of extremes = Product of means

a x d = b x c

(i) Third Proportion: if a:b = b:c, then c is called as the third proportion to a and b.

(ii) Mean Proportional: Mean proportional between a and b is √ (a x b)

(iii) Fourth Proportional: If a:b=c:d, then d is called the fourth proportional to a,b,c

(i) Comparison of Ratios: if (a:b) > (c:d), then (a/b) > (c/d)

(ii) Compounded Ratio: Consider the ratio, (a:b), (c:d), (e:f) then (a c e : b d f) is called as compounded ratio .

(i) Duplicate ratio of (a:b) is (a2:b2)

(ii) Sub Duplicate ratio of (a:b) is (√a: √b)

(iii) Triplicate ratio of (a:b) is (a3:b3)

(iv) Sub Triplicate ratio of (a:b) is (3√a : 3√b)

(v) If a/b = c/d, then, (a+b)/(a-b)=(c+d)/(c-d) . This is called as Componendo – Dividendo Rule

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