Question

There are two examination halls $-$ $M$ and $N$. If $10$ students are sent from $M$ to $N$, the number of students in both the halls is same. If $20$ students are sent from $N$ to $M$, the number of students in $M$ become twice the number of students in $N$. The number of students in $M$ and $N$ respectively are:

• A. $90,70$
• B. $80,60$
• C. $100,80$
• D. $120,80$
  

Answer 1

Answer: (C)

$100,80$

Let number of students in $M$ and $N$ be $x$ and $y$ respectively.
Now,
$x-10=y+10$
$x-y=20...\left(i\right)$
and,
$x+20=2\ast (y-20)$
$x+20=2y-40$
$x-2y=-60...\left(ii\right)$
Equation $\left(i\right)-\left(ii\right)$
$x-y-x+2y=20+60$
$\Rightarrow y=80$
Putting the value of $y$ in eq. $\left(i\right)$, we get
$x-80=20$
$\Rightarrow x=100$
So, number of students in $M$ and $N$ are $100$ and $80$.