If a : b = c : d, then which of the following ratio is equal to a : c ?

a + b : c + d 

a : b = c : d

\(\frac{a}{b}\)  =  \(\frac{c}{d}\)            ----- (i)

\(\frac{a}{c}\)  =  \(\frac{b}{d}\)            ------ (ii)

Adding 1 on both sides in eq(i),

\(\frac{a}{b}\) + 1 = \(\frac{c}{d}\) + 1 

\(\frac{a+b}{b}\)   = \(\frac{c+d}{d}\)

\(\frac{b}{d}\)        = \(\frac{a+b}{c+d}\)  ----- (iii)

From eq(ii), (iii)

a : c = a + b : c + d