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Note for Ratio and Proportion - RP by Placement Factory

  • Ratio and Proportion - RP
  • Note
  • Quantitative Aptitude
  • Placement Preparation
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Contents 1. 2. 3. 4. 5. 6. 7. Preface…………………………………………………………………………………..……2 Contents……………………………………………………………………………………..3 Introduction………………………………………………………………………………..4 What is Ratio?..…………………………………………………………………………..4 The Fundamental Property of Ratio….…………………………………………5 AnImportantResult……………………………………………………………………..5 Questions.…………………………………………………………………………………..5 Page 3 of 27

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Introduction: The Ratio could be perceived as a special case of percentage. All the concept related to approaching the of the Ratio questions could be easily correlated with the approach what we had already developed in the percentage Digi-notes (Specially the application of the Unitary Method). Like percentage; ratio is extensively used in the Data Analysis. So you are advised to go through the chapter thoroughly keeping in mind to learn how we are approaching the question. What is Ratio?: Page 4 of 27

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 Mathematically:  Let a and b be the two quantities.  Then ratio of a and b is defined as the fraction a b .  This fraction is simply denoted as a : b when we are talking about the ratio.  And is is read as “a is to b”.  Practically:  Since with the help of the fractions we are making comparison between the quantities, therefore ratio is the comparison between two quantities. The fundamental Property of Ratio:  As the multiplication or division by the same number to the numerator and denominator doesn’t affect a faction; in the same way the multiplication or division of each term of ratio by the same non-zero number doesn’t affect the ratio. An Important Result: I st Ratio  A : B  a : b II Ratio  B : C  c : d  Then combined Ratio  A : B : C  ac : bc : bd nd  It is to be noted that the individual ratios to be combined:  Should have one quantity in common.  And the common quantity of the Ist ratio should be at the second place and that of the IInd ratio at the first place. Questions: Page 5 of 27

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Que: If A, B, C are three quantities such that A:B = 5:4 and B:C = 3:2, find: 1) B : C 2) A : C 3) (A + B) : (A - C) Sol: We have 𝐴 ∶ 𝐵 ∶ 𝐶 = 5 × 3 ∶ 3 × 4 ∶ 4 × 2 = 15 ∶ 12 ∶ 8 Hence 1) B ∶ C = 12 ∶ 8 = 3 ∶ 2 2) A ∶ C = 15 ∶ 8 3) (A + B): (A − C) = (15 + 12): (15 − 8) = 27 ∶ 7 Que: The sum of the money with A and B is Rs.500. If the ratio of the money they had is 3:2, find the share of A. Sol: 𝐴= 𝑅𝑠.500 (3+2) × 3 = 𝑅𝑠. 300 Page 6 of 27

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