if a b c a 6 7 8 and 14 then..., Ratio & Proportion, General Mathematics

Question:If `a + b : b + c : c + a = 6 : 7 : 8` and `a + b + c = 14`, then the value of `c` is :

A `6` 
B `7` 
C `8` 
D `14`

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+ AnswerA

+ ExplanationLet `(a + b) = 6k`,

`b + c = 7k` and 

`c + a = 8k`.

Then,`2(a + b + c) = 21k`

or `2 xx 14 = 21k`

or `k = 4/3`.

`:. a + b = (6 xx 4/3) = 8`.

So, `c = (a + b + c) - (a + b)`

`= (14 - 8)`

`= 6`.

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