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If (ma + nb): b :: (mc + nd): d, prove that a, b, c, d are in proportion.
If (ma + nb): b :: (mc + nd): d, prove that a, b, c, d are in proportion.
Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
If (ma + nb): b :: (mc + nd): d, prove that a, b, c, d are in proportion.

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.

i

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