If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14,

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If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then find c ?

1. 6
2. 7
3. 8
4. 10

Correct Option: D

Let a + b = 6k, b + c = 7k, c + a = 8k ...(i)
and a + b + c = 14 ...(ii)

From Eq. (i),
a + b + b + c + c + a = 6K + 7K + 8K
⇒ 2(a + b + c) = 21K
⇒ 2 x 14 = 21K
⇒ K = 28/21 = 4/3

⇒ a + b 6k = = 6 x 4/32 = 8
Subtracting Eq. (iii) from Eq. (ii), we get
(a + b + c) - (a + b) = 14 - 8 = 6