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Q.

The two exam rooms, A and B, both contain some pupils. Ten pupils are sent from A to B in order to equalize the number of students in each hall. However, if 20 students are transferred from B to A, A will now have twice as many pupils as B. Find out how many students are in each of the two rooms.


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a

A=90 and B=70

b

A=100 and B=80

c

A=50 and B=30

d

A=60 and B=40 

answer is B.

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Detailed Solution

It is given that ten students are sent from room A to room B in order to equalize the number of students in each exam room.
Let's assume that there are m and n students in rooms A and B, respectively.
Since, 10 students are sent from A to B then the number of students is A will be decreased by 10 and that of B will be increased by 10. So,
n+10=m-10                                                                                                                                                                                                             ⇒m-n=20
⇒m=n+20      …1
Also, 20 students are sent from B to A then,
m+20=2(n-20) ⇒m+20=2n-40 ⇒m=2n-60            … (2)
On solving equation (1) and equation (1) we get,
n=80 Substitute n=80 in the equation (1) we get,
m=80+20=100 Therefore, the number of students in rooms A and B are 100 and 80 respectively.
Hence, option 2 is correct.
 
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