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?

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