Question

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

Answer 1

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

ma + nb/b = mc + nd/d

Then,cross multiply each other

d(ma+nb) = b(mc+nd)
mad + nbd = mcb + nbd
Cancelling (nbd) from both sides

mad = mcb
Cancelling m from both sides

ad = cb
a/b = c/d. -Hence proved

Answer 2

Here is your solution :

Given,

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

(Product of extremes= Product of means)

Mean = b and ( mc + nd )

Extremes= ( ma + nb ) and d


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

=> mad + nbd = mbc + nbd

=> mad = mbc + nbd - nbd

=> mad = mbc

=> ad = mbc ÷ m

=> ad = bc

=> a/b = c/d

•°• a : b : : c : d

Proved !!