Aptitude - Simplification - Discussion

Discussion :: 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:

[A]. 20
[B]. 80
[C]. 100
[D]. 200

Answer: Option C

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.


Doss said: (Feb 3, 2011)  
Dear friend explain with example.........

Prakash said: (May 9, 2011)  
I don't know how 2 was came at step 2.

Please explain.

Rcahana said: (May 25, 2011)  
Please help me solve this.

Akilapriya said: (Jul 15, 2011)  
I can't understand the sentence "then the number of students in A is double the number of students in B" explain me.

Mmmm said: (Jul 27, 2011)  
Tell me clearly. Please.

Sundar said: (Jul 30, 2011)  
Assume x,y

x-a, y-b

10 students from b-a. So x-b,then y+b

Now doubled

2(y-20) then both equation solved.

Prasu said: (Sep 19, 2011)  
Based on the answer a=100 and b=80. They said that if 20 sent from a to b then.

A will become double of b.

So if 20 sent then a=120 and b=60 i.e. a is double of b.

Basheerbi said: (Sep 23, 2011)  
I can't understand the prasu explanation tell me clearly.

Sandy said: (Oct 4, 2011)  
Can you explain by assuming a = 100?

Raji said: (Oct 11, 2011)  
Take these two cases individually let us look first through options 1st option is 20 so to apply both conditions is not possible so come to 80 so given if 10 people are sent to b then people in both class rooms are same so definetly b will be 60.

So again now apply second condition individually so by sending 20 people 4rm b A is twice that of B so this condition is not satisfied so now take 100 and check then both conditions satisfy and hence ans is 100

Raji said: (Oct 11, 2011)  
Its simple given second condition that by sending 20 people A is twice of B so A+20=2(B-20) and solving both conditions we get 100

Sumeet Kumar said: (Feb 17, 2012)  
Amigos..

Then the number of students in A is double the number of students in B.

Just use is equal to "=" instead of "is" After A and then think of it.

Easy isn't it.

Gurpreet said: (May 25, 2012)  
I didn't understand Solving (i) and (ii) we get: x = 100, why = 80. How?

Kalai said: (May 31, 2012)  
10 students moving from A to B


( decrease 10 from A & add 10 to B)
Then, A - 10 = B + 10 A - B = 20 .... (i)

20 Students moving B to A.(Note: After deducting 20 from B , A will be double) .

A + 20 = 2(B - 20)

A - 2B = -60 .... (ii)


====>

Solving (i) and (ii) we get: A = 100 , B = 80.

The required answer A = 100.

Pari said: (Oct 30, 2012)  
They said the number of students in A is double the number of students in B. We should multiply A by 2 instead of multiplying B by 2. Why we are multiplying A by 2? Please tell me.

Syed Taher Zama said: (May 14, 2013)  
To solve equations:

(A part) (B part)
x + 20 = 2(y - 20)
20 candidates are sent from B to A,so we are adding 20 to x,and because we are sending 20 students to A it gets doubled(A=2B).
And
For solving equations just subtract both.

x - y = 20 .... (i)

x - 2y = -60 .... (ii)

You will get y=80 and then substitute in eq(i) you will get x=100.

Selvi said: (Jul 2, 2013)  
Please explain me, how to solve (i) & (ii) and how get x=100 & y=80?

Vinshashee said: (Aug 30, 2013)  
When 20 students sent from B to A,

Then A become twice then of B.

Thats The Reason We take 2 in the second step.

Nandhakumar said: (Oct 26, 2013)  
Then the number of students in A is double the number of students in B" so the step was look like 2(x+20) = (y-20). Then how it come(x+20) = 2(y-20).

Tamil said: (Feb 3, 2014)  
x-y = 20 ------------(1).
x-2y = -60 ------------(2).

Solving (1) - (2),

x -y = 20----(1).
x -2y = -60----(2).
---------------
y = 80.
---------------
(If you want to solve two equations in any problem you must change sing of (2)nd equation without fail.)

Now you substitute the y value in (1)st or (2)nd equations as you like then you will get the value of x as 100.

x - y = 20-----(1).
y = 80.

so, x - 80 = 20.
x = 20+80.
x = 100.

Now you got it @Selvi.

Rama said: (Oct 4, 2014)  
If you don't mine, somebody please explain this in clear cut. First of all I can't understand the question.

Ash said: (Oct 27, 2014)  
First of all.

Let the no of students in room A = x; B=y.

A sent 10 students to b....i.e. x-10 = y+10.

Take y to left side and -10 to right side.

It becomes x-y = 20.....equation 1.

Then B sent 20 students to A....i.e. 2x+20 = 2(y-20).

In questions it is mentioned that after sending 20 students A have Double no of students.

That's why we are using 2 here now write equation as,

x+20 = 2(y-20).

x+20 = 2y-40.

Bring 2y-40 to left side,

x-2y+20+40 = 0.

We can write it as,

x-2y = -60.....equation 2.

Now solve equation 1&2,
x-y = 20.
x-2y = -60.
_____________
y = 80.

Now substitute y = 80 in equation 1 or 2.

x-80 = 20.

Therefore x = 100.

Hope you understand this @RAMA.

Swetha said: (Dec 28, 2014)  
First read the question 1 time.

A = x; B=y.

'A' sent 10 students to 'B' => x-10 = y+10.

We solve the equation as x-y = 20. It becomes equation 1.

Then 'B' sent 20 students to 'A' => x+20 = 2(y-20).

The number of students in 'A' is double the number of students in 'B'.

x+20 = 2(y-20).

We simply the equation as x+20 = 2y-40.

Bring 2y-40 to left side,

x-2y+20+40 = 0.

We solve the equation as x-2y = -60.......equation 2.

Now solve equation 1&2,

x-y = 20.

x-2y = -60.
_____________.

y = 80.

Now we substitute y = 80 in equation 1 or 2.

x-80 = 20.

x = 100.

Devicky said: (Jan 1, 2015)  
In this a to b represents the equation x-10 = y+10.

In this b to a represents the equation x+20 = 2(y-20).

Solving 2 equation we get the answer.

Anup said: (Jan 26, 2015)  
Everyone is going directly from solve equation 1&2,

x-y = 20.
x-2y = -60.

And result is y = 80 and x = 100.

No one explain how to solve this. What is the best formula to solve this. If you have no idea how to solve those equation don't write the same word again and again in comments here.

Prashant said: (May 10, 2015)  
It is very simple assume maximum capacity of seats in both room is 100, now A:B = 100:80.

There is no need to think about 1st equation or second just do maximum-lesser no. of side.

Prashant said: (May 10, 2015)  
Assume maximum capacity of both side 100 and subtract 20 from it a:b = 100:80.

Manish Kumar said: (Jul 15, 2015)  
I couldn't get how we solve both equation please make it clear by multiply.

Idhaa said: (Nov 4, 2015)  
2 has come because there are two rooms in the question.

Chandrasekhar said: (Mar 25, 2016)  
Students sent from A to B = 10;

Then A-10 = B+10; ---- (i)

Students sent from b to a = 20; then,

B-20 = A+20; --- (ii).

A is double no.of students in B so,

2(B-20) = A+20.

Solve 1 & 2, we get,

A = 100.

Naveena said: (Jun 22, 2016)  
Friends you are doing upto x and why values. But we have to double the A also comparing to B.

Kavya said: (Aug 2, 2016)  
It is A which is double. So the equation should be 2 (x + 20) = y - 20. Right?

Cgyel said: (Aug 3, 2016)  
If A is double then, Why 2 (y - 20)?

Ramesh.Mariyada said: (Oct 14, 2016)  
Exactly I have the same doubt as same as @Nandhakumar.

Can anyone help us?

Rajesh said: (Nov 1, 2016)  
We can find out the answer by option if the 1st option is 80. Consider the student of class B and transfer 10 students then in both the class are equal so definitely, A class has a 100 student then tally it.

Manojkumar said: (Nov 14, 2016)  
I know everyone understood the first part, but in the second part, some might find difficult to understand why we are doubling in why part rather than the x part. Here is my view.

Read the question very very slowly.

Here they told, "If 20 candidates are sent from B to A, then the number of students in A is double the number in B". So x+20 = 2 (y - 20).

So for those who argue it should be 2 (x + 20) = y - 20, then the question would be below.

"If 20 candidates are sent from B to A, then the number of students in A is doubled (the remain details about B would have been ignored).

I hope it clear your doubts.

Srividya said: (Nov 24, 2016)  
Friends as the question had given that A is doubled then why we doubled B? Can anyone explain this problem in another process?

Suman said: (Nov 25, 2016)  
Well explained @Tamil.

Koteswararao Chimmili said: (Dec 5, 2016)  
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

Shiv Mohan Sharma said: (Jun 20, 2017)  
Explain how to solve equ.1 and equ.2?

Akshay said: (Jun 21, 2017)  
Nice explanation, Thanks @Manojkumar.

Shanthini said: (Jun 22, 2017)  
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).

Geetha said: (Jul 2, 2017)  
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.

Sreeram said: (Jul 31, 2017)  
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.

Tuan said: (Aug 2, 2017)  
I don't understand this, please explain me.

Temmy said: (Aug 3, 2017)  
How did they get the y=80?

Tuan Ossen said: (Aug 6, 2017)  
I don't understand, Please explain me with proper guidance.

Naidu said: (Aug 12, 2017)  
Why we have to change the signs could anyone please explain?

Hiranmoy said: (Nov 6, 2017)  
X-10 = y+10.
X-y = 10+10.
=20 (i).

Then, x+20 = 2(y-20)
x-2y = 40
x-y = 2x40
x-y = 80 (ii).

Now adding (i) &(ii) we get 20+80 = 100.

Srinu said: (Mar 19, 2018)  
Nice explanation. Thanks.

Geethanjali said: (May 21, 2018)  
Simple to understand Thank you @Hiranmoy.

Garry said: (Aug 15, 2018)  
Accroding to last condtion, It should be 2(x+20).

Nagesh V said: (Oct 25, 2018)  
Thank for you answer @Ash.

Kaleem said: (Dec 16, 2018)  
Thank you all.

Saurya said: (Apr 26, 2019)  
Thank all for explaining.

Naga Invy said: (Jun 6, 2019)  
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.
A = 100 ----------------> answer

Sarvesh said: (Jul 12, 2019)  
Thank you @Naga.

Chandu said: (Jul 15, 2019)  
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.

Geetha said: (Aug 3, 2019)  
Please Explain the 2nd step.

Sagar said: (Aug 4, 2019)  
Thanks @Naga invy.

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