Published on January 26th, 2013 In category Education | Maths

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How to solve problems on ratio, proportion and variation

ratio proportions variationsRatio of the two terms is denoted by a:b and is measured by a/b. The a in the numerator is called as antecedent and the denominator b is called as consequent.

The ratio basically means how many multiples or parts is a of b. 

Proportion:  The numbers are in proportion when two ratios of the two terms are equal to ratio of other two terms, if a:b=c:d then a,b,c and d are in proportions

Variations:  The 2 quantities are said to be in direct or inverse proportion (variation) when a change in one quantity directly effects the other one. There can be direct effect that is known as direct proportion ( Like increase in “a” causes increase in “b”) and Inverse proportion when ( increase in “a” causes decrease in b). 

Have understood what is meant by Ratio, Proportion and Variations: we will consider some important points and rules related to these subjects

Ratios:  Some important points are as follows:

  • Both the antecedent and consequent should be in the same unit of measure
    • If the units are given in different measures then we need to combine units by compounding. e.g. ( m:n) and (a:b) then compounded ratio is (mxa)/(nxb) 
  • Ratio would remain unchanged when a constant number is multiplied or divided by antecedent or consequent

Some imp. Rules for Ratios

Rules for Ratio

Rules of Invertendo, Atlterendo, Componendo, Dividendo and Compendo and Dividendo in Ratios

Invertendo, Compnendo, Dividendo, Alternendo Ratios

Important Rules for Proportions:

1. If a:b=c:d then ad = bc

2. If in case we have a:b=b:c then this is a case of continued proportions and we can have b2 = ac, thus we can say b is mean of “a” and “c” and can be called as mean proportional

The concept of mean proportional and continued proportions can be useful finding one of the missing ratios in a set of 4 ratios for e.g.

Continued Proportions

Important rules on Variations are as follows:

 Rules for variations and proportions

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