The students in the three sections A, B and C of Class X are in the ratio 5 : 4 : 7. If 15, 16 and 9 new students are admitted to sections A, B and C, respectively, the ratio changes to 10 : 9 : 11. What is the total number of students in Class X after the new admissions?

Correct option is B

Given:
Students in sections A : B : C = 5 : 4 : 7
New students admitted:
Section A = 15
Section B = 16
Section C = 9
New ratio after admission = 10 : 9 : 11
Formula Used:​
If quantities are in ratio a : b : c, they can be written as ak, bk, ck
Solution:
Let the initial number of students be:
A = 5x
B = 4x
C = 7x
After admission, number of students becomes:
A = 5x + 15
B = 4x + 16
C = 7x + 9
According to the new ratio:
​$$\frac{5x + 15}{10} = \frac{4x + 16}{9}\\\ \\9(5x + 15) = 10(4x + 16)\\\ \\45x + 135 = 40x + 160\\\ \\5x = 25\\\ \\x = 5$$​​
Now,
A = 5×5 + 15 = 40
B = 4×5 + 16 = 36
C = 7×5 + 9 = 44
Total students after admission = 40 + 36 + 44 = 120
Total number of students = 120