If (a + b) : (b + c) : (c + a) = 3 : 6 : 5 and 2a + 3b = 40, then b is equal to ?

10 8 9 12

10

a + b = 3R, b + c = 6R, c + a =5R Adding all of above, we get: 2(a + b + c) = 14R (a + b + c) = 7R      ...............(i) b + c = 6R   ...........(ii) (i) - (ii) a = 1R, similarly b = 2R,  c = 4R Now, ⇒  2a +  3b = 40 ⇒  (2 × 1R) +  (3 × 2R) = 40 ⇒  2R  + 6R = 40 ⇒  8R = 40 ⇒  1R = 5  Here, b  = 2R = 2 × 5 = 10