The ratio of the numbers of boys and girls in a school was 5 : 3. Some new boys and girls were admitted to the school , in the ratio 5 : 7. At this , the total number of students in the school became 1200, and the ratio of boys to girls changed to 7 : 5. The number of students in the school before new admissions was
1). 700
2). 720
3). 900
4). 960
Let the original number of boys and girls be 5x and 3x respectively and that of new boys and girls be 5y and 7y respectively.
$\therefore$ 5x + 3x + 5y + 7y = 1200
=> 2x + 3y = 300 ............(i)
and, $\frac{5x+5}{3x+7y}$ = $\frac{7}{5}$
=> 25x + 25y = 21x + 49y
=> 4x = 24y
=> x = 6y ......... (ii)
From equation (i),
4x + 6y = 600
=> 5x = 600
=> x = 120
$\therefore$ Original number of students= 8x = 960