Question

Two persons $A$ and $B$ both have same pencils. If $A$ gives $10$ pencils to $B$, then $B$ will have twice as many as $A$. If $B$ gives $10$ pencils to $A$, then they will have the same number of pencils. How many pencils does each one has?

Answer 1

Let $A$ have $x$ pencils and let $B$ have $y$ pencils.

When $A$ gives $10$ pencils to $B$, he is left with $x-10$ pencils and $B$ has $y+10$ pencils.

The first condition is $y+10=2(x-10)$.
If $B$ gives $10$ pencils to $A$, then $B$ has $y-10$ and $A$ has $x+10$ pencils. The second condition says
$y-10=x+10$.
Thus we get two equations
$2x-y=\mathrm{30.....}\left(1\right)$
$y-x=\mathrm{20.......}\left(2\right)$
Adding the equations $\left(1\right)$ and $\left(2\right)$, we obtain $x=50$.

Using the equation $\left(2\right)$, we obtain $y=x+20=50+20=70$.
Thus $A$ has $50$ pencils and $B$ has $70$ pencils.