Question

There are 50 students in an auditorium, of which 2x are boys and y are girls. After (y - 6) boys leave the auditorium and (2x - 5) girls enter the auditorium, the probability of selecting a girl at random becomes 9/13. Find the value of x and of y?

Answer 1

Total number of students=50
Number of boys=2x
Number of girls=y
total will be:
2x+y=50
⇒y=50-2x

when (y-6) boys left the auditorium the new number of boys was:
2x-(y-6)
=2x-y+6
but y=50-2x
thus the new number will be:
2x-(50-2x)+6
=4x-44

when (2x-5) girls left the auditorium the remaining number will be:
y-(2x-5)
=y-2x+5
but 
y=50-2x
thus the new number of girls will be:
50-2x-2x+5
=55-4x
new total number of students:
(55-4x)+(4x-44)
=11

probability of selecting a girl at random will be:
(55-4x)/11=9/13
13(55-4x)=9*11
715-52x=99
616=52x
x=12
thus
y=50-12=38
thus
x=12 and y=38