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.

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x = 300 and y = 60

x = 200 and y = 70

x = 150 and y = 90

x = 100 and y = 80

answer is D.

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Detailed Solution

Given that 10 students from A to B:
Number of students in A = B
20 students from B to A:
Number of students in A = 2 B
Let, the number of students in halls A and B is x and y, then,

x − 10 = y + 10 ⇒ x − y = 20 … (i) (x + 20) = 2 (y − 20) ⇒ x − 2 y = − 60 … (i i)

On solving the above two equations, we get

x = 100

and

y = 80

Therefore, the number of students in the two halls is

x = 100 and y = 80

Hence, option (4) is correct.

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