Ratio and Proportion Questions Answers Formulas, Tips and Tricks

• 1. What is Ratio

  
  

  The ratio of two quantities a and b in the same units, is the fraction \begin{aligned} \frac{a}{b} \end{aligned} and we write it as a : b.
  
  In the ratio a : b, we call a as the first term which is also know as antecedent and b, the second term which is also called consequent.
  
  For example:
  \begin{aligned}
  4:5 = \frac{4}{5}
  \end{aligned}
  Here 4 is antecedent and 5 is consequent
  
  Important Rule :
  The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
  
  For example: 2:3 = 4:6 = 6:9

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• 2. What is Proprotion

  
  

  Equality of two ratios is called proportion.
  
  The equality of two ratios is called proportion.
  
  If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.
  
  Here a and d are called extremes, while b and c are called mean terms.
  
  Product of means = Product of extremes.
  Thus, a : b :: c : d <=> (b x c) = (a x d).

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• 3. Fourth, third and mean proportional

  
  

  i). Fourth Proportional:
  
  If a : b = c : d, then d is called the fourth proportional to a, b, c.
  
  ii). Third Proportional:
  
  a : b = c : d, then c is called the third proportion to a and b.
  
  iii). Mean Proportional:
  
  Mean proportional between a and b is \begin{aligned} \sqrt{ab} \end{aligned}

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• 4. Comparison of Ratios and Compounded Ratio

  
  

  i). Comparison of Ratios:
  When we say that a:b > c:d, then it means
  \begin{aligned}
  \frac{a}{b} > \frac{c}{d}
  \end{aligned}
  
  ii). Compounded Ratio:
  The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf)
  
  Please note it is ratio of first ratio term of every ratio and second ratio term of every ratio

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• 5. Important results of Ratio

  
  

  i). Duplicate ratio of (a:b) is
  \begin{aligned}
  (a^2:b^2)
  \end{aligned}
  
  ii). Sub-duplicate ratio of (a : b) is
  \begin{aligned}
  (\sqrt{a}:\sqrt{b})
  \end{aligned}
  
  iii). Triplicate ratio of (a : b) is
  \begin{aligned}
  ({a}^3:{b}^3)
  \end{aligned}
  
  iv). Sub Triplicate ratio of (a : b) is
  \begin{aligned}
  ({a}^\frac{1}{3}:{b}^\frac{1}{3})
  \end{aligned}
  
  v).
  \begin{aligned} if& \frac{a}{b} = \frac{c}{d}, \\
  then \frac{a+b}{a-b} = \frac{c+d}{c-d}
  
  \end{aligned}

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• 6. Ratio Variation

  
  

  i). We say that x is directly proportional to y, if x = ky for some constant k and we write,
  \begin{aligned}
  x \propto y
  \end{aligned}
  
  ii). We say that x is inversely proportional to y, if xy = k for some constant k and
  we write
  
  \begin{aligned}
  x \propto \frac{1}{y}
  \end{aligned}

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Ratio and Proportion Questions Answers