Aptitude - Simplification - Discussion

Anyone, please help me to get the answer.

The students first sent from room A to B means 10 students sent from A to B so the number is equal between them just multiply;
i.e 10 × 10 = 100.

Then it's said from B to A they sent 20 students and A got double that B.
i.e 100 - 20 = 80.

Then the number of students in A is double the number of students in B. This is because 2 (y-20).

When 10 are sent from A to B. A loses and B gains.

A -10 = B+10...
= A - B = 20---> 1

When 20 are sent from B to A. A gains and B loses. But A gains twice as much as B has. Therefore A = 2B.
A+20 = 2(B-20)...
=> A-2B = -40-20 = A-2B=-60 ---> 2

Use elimination to solve equations a and b simultaneously
A-B = 20 (NOTE: When 2 -s meet, they become +)
-A-2B=-60
................
B = 80 (from 20--60 = 20+60)

Substitute B= 80 into eqtn 1
A - 80 = 20
A= 20 + 80 = 100.

Therefore, A =100, and B = 80.

If B has 80 students and 20 are taken to A which has 100, we get:
A+20 = B-20.
100+20 = 80-20.
120 = 60.
Therefore, room A has twice than B.

By Solving (i) and (ii) we get: x = 100, y = 80.

The required answer A = 100.

Let's c option C i.e. 100.
A exam hall ----------- B exam hall
100 ----------- 80
10 from A to B = 90 | 90.

1st condition satisfies:

Let's see the 2nd condition:
If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B.

A exam hall ----------- B exam hall
100 ----------- 80.

20from B to A = 120(100+20) | 60(80-20).

Therefore 100 is the right answer.

I disagree, if A is double the number of B.

How can 100 be the answer?

As B is 60 if we double it we get 160.

If 2A=B, Also A=2B.

A=80, B=40, in other words: A=40*2=80.

x-y=20
x=20+y ---> (1)
x-2y=-60 ---> (2)
20+y-2y=-60 --->(3)

+y-2y=-60-20
-y=-80
y=80
Sub value of y in eqn 1, we get;
x=20+80 = 100.

Hello, can you please explain the last step i.e x=100 y=80?