If-x-y-x-y-z-y-z-x-y-z-x-z-x-y-z-p-then-which-of-the-following-can-be-the-value-of-p-

Question Number 8230 by 314159 last updated on 03/Oct/16

If \frac{x + y}{x + y + z} = \frac{y + z}{x + y + z} = \frac{x + z}{x + y + z} = p, then which of

the following can be the value of p ?

Answered by Rasheed Soomro last updated on 03/Oct/16

\frac{a}{A} = \frac{b}{B} = \frac{c}{C} = \frac{a + b + c}{A + B + C}

p = \frac{x + y}{x + y + z} = \frac{y + z}{x + y + z} = \frac{x + z}{x + y + z}

= \frac{(x + y) + (y + z) + (x + z)}{(x + y + z) + (x + y + z) + (x + y + z)}

= \frac{2 x + 2 y + 2 z}{3 (x + y + z)} = \frac{2 (x + y + z)}{3 (x + y + z)} = \frac{2}{3}