Question

Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.

• A. $100,80$
• B. $80,100$
• C. $110,70$
• D. $70,110$
• E. None of these

Answer 1

Answer: (A)

$100,80$

Let the number of students in $A$ and $B$ be $a\&b$ respectively.
As per the question:

$a-10=b+10$
$a-b=20...\left(i\right)$
and

$a+20=2(b-20)$
$a-2b=-\mathrm{60.....}\left(ii\right)$
Since coefficient of $a$ is same in both equations, we can subract $\left(ii\right)$ from $\left(i\right)$.

$\left(i\right)-\left(ii\right):$
$a-b-(a-2b)=20-(-60)$
$⟹b=80$

$a=80+20=100$