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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 120.
Let initial numbers = 5x, 4x, 7x
After admissions: 5x + 15 : 4x + 16 : 7x + 9 = 10 : 9 : 11
Let common multiplier = t
5x + 15 = 10 t
4x + 16 = 9 t
From first: 5x + 15 = 10 t ⇒ x = 2 t - 3
Substitute in second: 4(2 t - 3) + 16 = 9 t
8 t - 12 + 16 = 9 t
8 t + 4 = 9 t
t = 4
x = 2 × 4 - 3 = 5
Initial counts: 5x = 25, 4x = 20, 7x = 35
After admissions: 25 + 15 = 40
20 + 16 = 36
35 + 9 = 44
Total after admissions = 40 + 36 + 44 = 120