The number of students in 3 classes is in the ratio of 2:3:4. If 12 students are increased in each class this ratio changes to 8…

Question

The number of students in 3 classes is in the ratio of 2:3:4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was

1. A. 162 (Correct answer)
2. B. 108
3. C. 95
4. D. 54

Correct Answer

Option A — 162

Detailed Solution & Explanation

The correct answer is 162.

Key Points

• Let the original strengths be 2x, 3x and 4x.
• After adding 12 to each class: (2x + 12) : (3x + 12) : (4x + 12) = 8 : 11 : 14.
• Equating the first two ratios: 11(2x + 12) = 8(3x + 12) → 22x + 132 = 24x + 96 → 2x = 36 → x = 18.
• Original total = 2x + 3x + 4x = 9x = 9 x 18 = 162.

Additional Information

• Verification: the classes held 36, 54 and 72 students. Adding 12 gives 48, 66 and 84, and dividing through by 6 gives exactly 8 : 11 : 14.
• Always confirm the third ratio term as well — matching only the first two can occasionally admit a wrong value.