If ax+y=by+z=cz-x, then which of the following equations is true?

If $\frac{a}{x + y} = \frac{b}{y + z} = \frac{c}{z - x}$ , then which of the following equations is true?

A
$a = b + c$
B
$c = a + b$
C
$b = a \times c$
D
$b = a + c$

Solution:

Given equation is

\frac{a}{x + y} = \frac{b}{y + z} = \frac{c}{z - x}

.
Let

\frac{a}{x + y} = \frac{b}{y + z} = \frac{c}{z - x} = k

.
⇒

a = xk + yk

… (1)
⇒

b = yk + zk

… (2)
⇒

c = zk - xk

… (3)
Adding

(1), (3)

gives,
⇒

a + c = zk - xk + xk + yk

⇒

a + c = zk + yk

… (from 2).

∴

a + c = b

Hence, the correct option is 4.

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