Question

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

Answer 1

ma+nb = mc+nd
b d
=> d(ma+nb)=b(mc+nd)
=> dma+dnb=bmc+bnd
=> dma-bmc=bnd-dnb
=> m(da-bc)=n(bd-db)
=> m(da-bc)=n(0)
=> m(da-bc)=0
=> da-bc=0
m
=> da-bc=0
=> da=bc
=> a = c
b d
=> thus, a,b,c and d are in proportion.
hence proved
Hope it's help.