Question

If $\frac{x}{p}+q=\frac{y}{q}+p$ and $x=y,p\ne q,$ the value of $x$ or $y$ is

• A. $pq$
• B. $\frac{1}{pq}$
• C. $-pq$
• D. $-\frac{1}{pq}$

Answer 1

The correct option is C $-pq$

$\frac{x}{p}+q=\frac{y}{q}+p$ (1)

$x=y$ (2)

Substituting (2) in (1)

$\frac{x}{p}+q=\frac{x}{q}+p$

$\Rightarrow \frac{x}{p}-\frac{x}{q}=p-q$

$\Rightarrow x(\frac{1}{p}-\frac{1}{q})=p-q$

$\Rightarrow x\left(\frac{q-p}{pq}\right)=p-q$

$\Rightarrow \frac{-x}{pq}=1$

$\Rightarrow x=-pq$

Hence the correct option is (C).