Question

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

• A. 6
• B. 8
• C. 14
• D. 7

Answer 1

Answer: (A)

6

$\frac{a+b}{b+c}=\frac{6}{7}\frac{b+c}{c+a}=\frac{7}{8}$
$\Rightarrow 7a+7b=6b+6c\Rightarrow 8b+8c=7c+7a$
$\Rightarrow 7a+b=6c\to 1\Rightarrow 8b+c=7a\to 2$
Putting $2$ in $1$
$\Rightarrow 8b+c+b=6c$
$\Rightarrow \frac{9b}{5}=c\therefore b=\frac{5c}{9}$
$a+b+c=14$
$\Rightarrow \frac{8b+c}{7}+b+c=14$
$\Rightarrow \frac{8\times \frac{5c}{9}+c}{7}+\frac{5c}{9}+c=14$
Solving we get $c=6$