Question

If $\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=r$ then, r cannot take any value except :(CAT 2004)

• A.
• B. -1
• C. ½ or -1
• D. -1/2 or -1

Answer 1

The correct option is C ½ or -1

Option (c)

As $\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=\frac{a+b+c}{b+c+c+a+a+b}$

$=\frac{a+b+c}{2(a+b+c)}=r=\frac{1}{2}$ (Assuming a + b + c ≠ 0)

If a + b + c = 0

$\frac{a}{b+c}$ = $\frac{a}{a+b+c-a}$ (by adding and subtracting a in the denominator) $=\frac{a}{0-a}=\frac{a}{-a}=r=-1$

(similarly $\frac{b}{c+a}=\frac{c}{a+b}$= -1)

Hence r can take only $\frac{1}{2}$ or -1 as values. Choice (c)