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 whence 
m(ad -- bc) = n(bd -- bd) giving ad -- bc = 0 as m is not equal to 0. 
ad -- bc = 0 OR ad = bc OR a/b = c/d OR a : b :: c : d QED

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