# Aptitude - Simplification - Discussion

Discussion Forum : Simplification - General Questions (Q.No. 2)
2.
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
20
80
100
200
Explanation:

Let the number of students in rooms A and B be x and y respectively.

Then, x - 10 = y + 10      x - y = 20 .... (i)

and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

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

The required answer A = 100.

Discussion:
74 comments Page 2 of 8.

Hello said:   5 years ago
Where is Ramesh? The one who explained the previous question very simply in this same chapter.
(1)

Swathi hj said:   5 years ago
Why we take x-10 and y+10, can anyone tell me?
(1)

Prakash said:   5 years ago
Could you please explain this? I am not getting it.

Prakash said:   5 years ago
Could you please explain this? I am not getting it.

Sagar said:   5 years ago
Thanks @Naga invy.

Geetha said:   5 years ago

Chandu said:   5 years ago
We have to only subtract 10 students from A ie;A-10=B (OR) A=B+10.

But how do you add 10 to A sub 10 from B at a time that means 20 students are sending to B from A.

A-10=B,
B-20=2B=>B=20,
A-10=20,
A=30.
(1)

Sarvesh said:   5 years ago
Thank you @Naga.

Naga Invy said:   5 years ago
If 10 students sent from room A to B; then;

step 1: A -10 = B +10
Step 2 : If you change the B and -10 vice versa then the equation will be
A - B = 10 +10
therefore (A - B = 20) -----------------> Equation (1)

If 20 students sent from room B to A; then A becomes double as size of B
Step 3 : A + 20 = 2 (B - 20)
Please understand we are adding 2 in front of (B -20) because question states A becomes double as size B.

Now solve the step 3;
Step 4 : A + 20 = 2B -40
By changing the values vice versa, it becomes
Step 5 : A - 2B = (-20-40)
Step 6 A -2B = -60 -------------------> Equation (2)

Now solve both Equation 1 and 2
A- B = 20 ---------------> (1)
A- 2B = -60 ---------------> (2)

By changing the signs of equation 2, it becomes
A - B = 20 ---------------> (1)
- A + 2B = + 60 ---------------> (2)
----------------------
B = 80
---------------------
Solve the B value in equation ------> 1 to get an answer

A - B= 20.
then,
A - 80 = 20.
A = 20+80.