Question

There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall, $10$ students are sent from $A$ to $B$. But if $20$ students are sent from $B$ to $A$, the number of students in $A$ becomes double the number of students in $B$. Find the number of students in the two halls.

• A. $100$ students in hall $A,80$ students in hall $B$
• B. $200$ students in hall $A,45$ students in hall $B$
• C. $80$ students in hall $A,70$ students in hall $B$
• D. $120$ students in hall $A,60$ students in hall $B$

Answer 1

The correct option is A $100$ students in hall $A,80$ students in hall $B$

Let the number of students in hall $A$ be $x$ and number of students in hall $B$ be $y$.

If $10$ students are send fro hall $A$ to $B$, Then the number of students in hall $A$ will be lessened by $10$ and that of $B$ will be increased by $10$.

The same will happen when $20$ students are send from hall $B$ to hall $A$.

Therefore, according to first case, we have

$x-10=y+10$

$x=y+20$ ....(1)

By second case, we have

$x+20=2(y-20)$

$x=2y-60$ ....(2)

Solving (1) and (2), we get

$y+20=2y-60$

$\Rightarrow y=80$

Putting $y=80$ in equation (1), we get

$x=80+20=100$

So, the number of students in hall $A=100$ and the number of students in hall $B=80$.