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
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.