Question

For the equation $\frac{a-x}{a}+\frac{2a-x}{2a}=\frac{3a-x}{3a}$, which of the following relation holds good?

• A. $6x=7a$
• B. $ax=0$
• C. $7x=6a$
• D. $a=x$

Answer 1

Answer: (C)

$7x=6a$

Given,

$\frac{a-x}{a}+\frac{2a-x}{2a}=\frac{3a-x}{3a}$
$⟹$ $a-x+\frac{2a-x}{2}=\frac{3a-x}{3}$.

Multiply both sides by the LCM of the denominators, i.e. LCM of $2,3=6$, we get,

$⟹$ $6(a-x)+3(2a-x)=2(3a-x)$
$⟹$ $6a-6x+6a-3x=6a-2x$ ...[By Distribution Law]

$⟹$ $12a-9x=6a-2x$.

Transposing $x$ terms to one side, we get,

$⟹$ $12a-6a=9x-2x$
$⟹$ $7x=6a$.

Hence, option $C$ is correct.