Aptitude - Simplification - Discussion

I don't understand, Please explain me with proper guidance.

Why we have to change the signs could anyone please explain?

Nice explanation, Thanks @Manojkumar.

See guys first take. x+10=2(y-40).
Then it comes as x-2y=-60,
First eq is x-y=20,

Solve both.
X-y=20,
x-2y=-60,

Change signs/
We get;
x-y=20,
-x+2y=60,
Then we get y=80,
Substitute in eq 1,
We get x=100.

I don't understand this, please explain me.

Assume A= 70 and B= 50.

Then according to question 10 students from A will be transferred to B so now they are going to b equal.
A=60 and B=60,
And if we transfer 20 students from B to A,
It's going to be A=80 and B=40 I.e A is double of B,
So why can't D answer be 80.

Friends I'll say one simple logic. If "is " is given after A then you must consider as A =. So as per question if we see means A is double the number of students in b.

So (x+20) =2 (y-20).

If 10 students are sent from A to B,then the number of students in each room is the same
a-10 = b+10 ; ---- (1)

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+20 = 2(b -20); ---- (2) ( suppose A=10,B=5 that means A=2B then 10=10 )

Equation 1

a-10 = b+10.
a-b = 20.

Equation 2

a+20 = 2(b-20)
a+20 = 2b -40
a-2b = -60.


Solving equation 1 and 2
a-b = 20
a-2b = -60 (-a+2b = +60)
_____________.
b = 80

b is substitute in equation 1
a - b = 20
a = 20 + b
a = 20 + 80
a = 100

The answer is a = 100

Nice explanation. Thanks.

Simple to understand Thank you @Hiranmoy.