UGC NET Questions (Paper – 1)

Let the original numbers of boys and girls be 7k and 5k. After 6 boys leave and 14 girls join, the new numbers are 7k − 6 and 5k + 14, and the ratio becomes 1:1. Hence 7k − 6 = 5k + 14, which gives 2k = 20 and k = 10. Therefore the original number of boys is 7k = 70. This matches the condition that the class becomes balanced after the given changes.

Option A:
Option A is correct because it is directly obtained from solving the linear equation formed by the new equal numbers of boys and girls. With 70 boys and 50 girls initially, removing 6 boys and adding 14 girls yields 64 boys and 64 girls. The ratio 64:64 is indeed 1:1, confirming the validity of 70 as the original boy strength.

Option B:
Option B, 64, represents the number of boys after 6 leave in the correct solution, not the original count. Treating 64 as the original figure would lead to a different number of boys after departure and thus fail to produce equality with the adjusted number of girls. Therefore 64 does not satisfy the original ratio 7:5 along with the transformation.

Option C:
Option C, 80, would give girls as (80 × 5/7) ≈ 57.14 to maintain the original ratio, which is not an integer and hence not viable for a headcount. Even if we forced integers near these values, the changed numbers would not become equal after subtracting and adding the specified students.

Option D:
Option D, 84, similarly leads to a non-integer girls count when used with ratio 7:5, and the subsequent changes would not result in a 1:1 ratio. This contradicts both the initial and final conditions, so 84 cannot be the original number of boys.