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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
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
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Let the number of people in A be x and in B be y.
When 10 people are sent from A to B,
x-10 = y+10
x-y = 20
When 20 people are sent from B to A,
x+20 = 2(y-20)
x+20 = 2y-40
x-2y = -60
x-y = 20
x-2y = -60
- + +
________
y = 80
x-80 = 20
x = 100
There are 100 people in A and 80 people in B.
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Answer :
Given,
1) There are two examination rooms - A and B
2) If 20 candidates are sent from B to A , then the no. of candidates in A is double of B.
2) If 10 students are sent from A to B , then no. of students is same in both rooms.
To find,
The no. of students in room A
Solution :
Let the no. of candidates in room A be x and no. of candidates in room.B be y.
Now, we will frame equations for both the two given conditions :-
1) 2 (y - 20) = x + 20 (i)
2) x - 10 = y + 10 (ii)
Now, we have two equations and two unknown variables.
From eq. (ii),
y + 10 = x - 10
y = x - 10 - 10
y = x - 20
Putting this value of y in (i)
2((x-20)-20)= x + 20
Solving for x:
2(x-40)=x+20
2x-80=x+20
2x-x=20+80
x=100
We know,
y=x-20 = 100-20 = 80
So , No. of students in room A = x = 100
Answer : 100 candidates / students.