If (a+b):(b+c):(c+a)=6:7:8, and (a+b+c)=14, then find the value of 'c'.

A)6

B)7

C)8

D)14

Let,

a + b = 6k...........................(1)

b + c = 7k...........................(2)

c + a = 8k...........................(3)

adding 1,2 and 3, we get

a + b + b + c + c + a = 6k + 7k + 8k

⇒2(a + b + c) = 21k

⇒(a + b + c) = 21k/2

but we have given a + b + c = 14

so, 21k/2 = 14

⇒k = 4/3

so a + b = 6 * 4/3  = 8

now c = (a + b + c) - (a + b)  = 14 - 8  = 6