There are some students in the two examinatio | vedclass

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Question

(A) Let the number of students in halls $A$ and $B$ be $x$ and $y$,respectively.According to the first condition,if $10$ students are sent from $A$ to

Vedclass · Accepted Answer

Hall $A = 100$,Hall $B = 80$

Vedclass · Answer

(A) Let the number of students in halls $A$ and $B$ be $x$ and $y$,respectively.According to the first condition,if $10$ students are sent from $A$ to $B$,the number of students becomes equal:$x - 10 = y + 10$$\Rightarrow x - y = 20$  ---$(i)$According to the second condition,if $20$ students are sent from $B$ to $A$,the number of students in $A$ becomes double the number of students in $B$:$x + 20 = 2(y - 20)$$x + 20 = 2y - 40$$\Rightarrow x - 2y = -60$  ---(ii)Subtracting equation (ii) from equation $(i)$:$(x - y) - (x - 2y) = 20 - (-60)$$x - y - x + 2y = 80$$y = 80$Substituting $y = 80$ in equation $(i)$:$x - 80 = 20$$x = 100$Thus,there are $100$ students in hall $A$ and $80$ students in hall $B$.

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