Question

30. The number of students in 3 classes are in the ratio 2 : 3:4. If 12 student
increased in each, this ratio changes to 8:11: 14. Find the total numb
students in the three classes in the beginning ?
(a) 54
(b) 108
(c) 96
(d) 162​

Answer 1

Let the number of students in the classes be 2x, 3x and 4x respectively

$Total \: students = 2x + 3x + 4x = 9x$

According to the Question

$\frac{2x + 12}{3x + 12} = \frac{8}{11}$

$= > (2x + 12) \times 11 = (3x + 12) \times 8$

$= > 22x + 132 = 24x + 96$

$= > 24x - 22x = 132 - 96$

$= > 2x = 36$

$= > x = \frac{36}{2}$

$= > x = 18$

So,

$Total \: Students = 9x = 9 \times 18 = 162$

Answer 2

Let the number of students in the classes be 2x, 3x and 4x respectively

$Total \: students = 2x + 3x + 4x = 9x$

According to the Question

$\frac{2x + 12}{3x + 12} = \frac{8}{11}$

$= > (2x + 12) \times 11 = (3x + 12) \times 8$

$= > 22x + 132 = 24x + 96$

$= > 24x - 22x = 132 - 96$

$= > 2x = 36$

$= > x = \frac{36}{2}$

$= > x = 18$

So,

$Total \: Students = 9x = 9 \times 18 = 162$