In a class room ,one third of the total students are boys .if one sixth of the boys and one fourth of girls are absent.then the number of students present is 28 what is the total number of students?
Answers
Let the total number of boys be x, and the total number of girls be y.
One third out of all students are boys,
So,
1/3(x+y) = x
=> x+y = 3x
=> y = 2x
One sixth of the boys are absent. So, number of boys present = x - (1/6)x
= (6x - 1x)/6
= 5x/6
One fourth of the girls are absent. So, number of girls present = y - (1/4)y
= (4y-1y)/4
= 3y/4
Total number of students present = 28
So,
5x/6 + 3y/4 = 28
(10x + 9y)/12 = 28
10x + 9y = 28*12
10x + 9y = 336
10x + 18x = 336 [y = 2x]
28x = 336
x = 12
So, number of girls y = 2x
y = 2*12 [ x = 12 ]
y = 24
Total number of students = x+y = 12 + 24 = 36 (ans.)
The answer is 36. I solved it by myself.