If a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7, then b : (a + c) is equal to :

1 : 2
$latex a : (b+c) = 1 : 3$
$latex => \frac{b+c}{a} = \frac{3}{1}&s=1$
$latex => \frac{b+c}{a}+1 = \frac{3}{1}+1&s=1$
$latex => \frac{a+b+c}{a} = \frac{3+1}{1} = \frac{4}{1}……(1)&s=1$
Similarly
$latex \frac{a+b}{c} = \frac{7}{5}&s=1$
$latex => \frac{a+b+c}{c} = \frac{12}{5}……(2)&s=1$
On dividing (1) by (2),
$latex \frac{c}{a} = \frac{4\times 5}{12} = \frac{5}{3} = k……(3)&s=1$
From equation (1), $latex b = 4k&s=1$
$latex \therefore \frac{b}{a+c} = \frac{4k}{3k+5k} = 1 : 2&s=1$
Hence option [C] is correct answer.