# Ratio and Proportion

Hence similar is with the aggregate values. â€¢If a number is to be proportionately changed in a given ratio then the antecedent refers to the given number. Hence find the proportionality constant (number / antecedent) and multiply this constant with the consequent to get the answer. If 25 is to be changed in ratio 5:7 then 25 is represented by 5, so constant is 25/5 = 5, hence answer is 5×7 = 35 â€¢In a given ratio a : b â€¢If a > b then ratio is of greater inequality â€¢If a < b then ratio is of lesser / less inequality.

The inverse ratio is b : a â€¢Duplicate ratio is a2 : b2 â€¢Triplicate ratio is a3 : b3 â€¢Subduplicate ratio is va : vb â€¢Subtriplicate ratio is 3va : 3vb â€¢Commensurable if a and b are integers â€¢Incommensurable if a and b are not integers â€¢The compounded ratio of (a1: b1), (a2 : b2) and (a3 : b3) is (a1. a2. a3) : (b1. b2. b3) [ that is product of the antecedents by product of the consequents ] â€¢A ratio, multiplied with its inverse produces 1. â€¢A ratio multiplied with itself produces duplicate ratio Continued ratio or proportion is the proportional relationship between 3 or more items.

Proportion brings about a continuous relationship between 3 or more items = relationship between 2 or more ratios â€¢Let A : B = 2 : 3 and B : C = 5 : 7 . then A : B : C ? 2 : 3 : 7 or ? 2 : 5 : 7 â€¢We need to bring parity at b and LCM of 3 and 5 is 15. So â€¢A 2 > 2 x 5 = 10 â€¢B 3 > 3 x 5 = 15 5 > 5 x 3 = 15 â€¢C 7 > 7 x 3 = 21 â€¢so A : B : C = 10 : 15 : 21 The mean proportion of A and B is X such that â€¢A, X and B are in proportion â€¢A, X and B are in geometric progression â€¢X is the geometric mean â€¢(A/X) = (X/B) â€¢X2 = AB â€¢In A : B : C : D â€¢A and D are called extremes / extreme terms â€¢B and C are called means / middle terms â€¢A, B, C and D are in a geometric progression â€¢(A/B) = (B/C) = (C/D) â€¢A. D = B. C that is (product of extremes) = (product of means) â€¢B2 = AC â€¢C2 = BD â€¢The third proportion of A and B is X such that â€¢A, B and X are in proportion â€¢A, B and X are in geometric progression B is the mean proportion of A and X â€¢(A/B) = (B/X) â€¢B2 = AX.