• # question_answer If $(a+b):(b+c):(c+a)=6:7:8$ and $a+b+c=14,$ then the value of ?c? is A)  8                    B)  7        C)  6        D)  12

[c] Let the ratio be k $\therefore$ $a+b=6k,\,\,b+c=7k,\,\,c+a=8k$ $\Rightarrow$ $(a+b)+(b+c)+(c+a)=6k+7k+8k$ $\Rightarrow$ $2(a+b+c)=21k$ $\Rightarrow$ $k=\frac{2\times 14}{21}=\frac{4}{3}$ $\therefore$ $c=(a+b+c)-(a+b)$ $=14-6\times \frac{4}{3}$ =14 ? 8 = 6