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If (ma + nb): b :: (mc + nd): d, prove that a, b, c, d are in proportion.

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exam oriented an important question from ML aggarwal, class 10th, chapter 7, ratio and proportion, Avichal publication

In this question we have been given that (ma + nb): b :: (mc + nd): d, and we have to prove that a, b, c, d are in proportion.

Question no 5, 7.3

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  1. Solution:

    It is given that

    (ma + nb): b :: (mc + nd): d

    We can write it as

    (ma + nb)/ b = (mc + nd)/ d

    By cross multiplication

    mad + nbd = mbc + nbd

    Here mad = mbc

    ad = bc

    By further calculation

    a/b = c/d

    Therefore, it is proved that a, b, c, d are in proportion.

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