if (a + b) : (b + c ) : (c + a) = 8 : 7 : 5 and a + b + c = 60, then the ratio of a : b : c is:

Explanation

Given: (a + b) : (b + c ) : (c + a) = 8 : 7 : 5 a + b + c = 60 Calculation: a+b=8 ----(i) b+ c=7 ----(ii) c+a=5 ----(iii) By adding eq (i), (ii) and (iii) we get, 2a + 2b + 2c = 20 ⇒ a + b + c = 10 Now, Here 10 = 60 So, 1 = 6 a+b=8×6 ⇒ 48 So, c = 60 - 48 ⇒ 12 Putting the value of c in the eq (ii) we get, b + 12 = 7 × 6 ⇒ b = 42 - 12 ⇒ b = 30 Now, a + 30 = 48 ⇒ a = 48 - 30 ⇒ a = 18 So, a : b : c = 18 : 30 : 12 ⇒3:5:2 ∴ The ratio of a : b : c is 3 : 5 : 2.