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Find the compounded ratio of: (i) 2: 3 and 4: 9 (ii) 4: 5, 5: 7 and 9: 11 (iii) (a – b): (a + b), (a + b)2: (a2 + b2) and (a4 – b4): (a2 – b2)2

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Question no.2  From ML aggarwal book, class10, chapter 7, ratio and proportion

We have been given two ratios in forms of a:b and c:d, and we have to find the compound ratio of them.

ML Aggarwal book

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  1. Solution:

    (i) 2: 3 and 4: 9

    We know that

    Compound ratio = 2/3 × 4/9

    = 8/27

    = 8: 27

    (ii) 4: 5, 5: 7 and 9: 11

    We know that

    Compound ratio = 4/5 × 5/7 × 9/11

    = 36/77

    = 36: 77

    (iii) (a – b): (a + b), (a + b)2: (a2 + b2) and (a4 – b4): (a2 – b2)2

    We know that

    Compound ratio = (a – b)/ (a + b) × (a + b)2/ (a2 + b2) × (a4 – b4)/ (a2 – b2)2

    By further calculation

    = (a – b)/ (a + b) × [(a + b) (a + b)]/ (a2 + b2) × [(a2 + b2) (a + b) (a – b)]/ [(a + b)2 (a – b)2]

    So we get

    = 1/1

    = 1: 1

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