Ratio and Proportion

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Ratio and Proportion

If 2 numbers are in ratio a: b then consider them as ax and bx (where x is the proportionality constant) and apply ax and bx in the given condition of the problem to proceed for answer

Ratio can be applied between 2 units if and only if the same physical quantity is compared •Length : length is correct
Length : density is wrong

Ratio can be made only after the units are compared in the same unit •If two lengths are 1 mile and 1 km respectively then ratio 1:1 is incorrect. •It should be 1.6:1 = 16:10 = 8:5 being converted to km

Ratio of a to b = a : b = a / b where a and b are the terms of ratio wherein a = first term = antecedent and b = second term = consequent

In a problem, to maintain the same ratio, if the antecedent is multiplied / divided by an integer / fraction then the consequent must be multiplied / divided by the same integer / fraction

Ratio is expressed in lowest terms.

As every number corresponds to its part in ratio, it is involved so the number of unit differences in the ratio, expressed in lowest terms, corresponds to the actual difference of true figures. Hence similar is with the aggregate values.

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 5x7 = 35

In a given ratio a : b
If a > b then ratio is of greater inequality
If a < b then ratio is of lesser / less inequality
The inverse ratio is b : a
Duplicate ratio is a2 : b2
Triplicate ratio is a3 : b3
Subduplicate ratio is √a : √b
Subtriplicate ratio is 3√a : 3√b
Commensurable if a and b are integers
Incommensurable if a and b are not integers

The compounded ratio of (a1: b1), (a2 : b2) and (a3 : b3)...
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