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

If a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7, then b : (a + c) is equal to :
[A]2 : 1
[B]2 : 3
[C]1 : 2
[D]1 : 3

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