UGC NET Questions (Paper – 1)

Let the numbers be 5x and 12x. Their difference is 12x − 5x = 7x, which is given as 133. Solving 7x = 133 gives x = 19. Hence, the numbers are 5 × 19 = 95 and 12 × 19 = 228, and the larger number is 228.

Option A:
Option A, 190, might be formed by doubling 95, but it does not fit the structure 12x with x = 19. If 190 were the larger number, the smaller under the 5:12 ratio would be 190 × (5/12) ≈ 79.17, and the difference would not be 133, so this choice is inconsistent.

Option B:
Option B, 209, cannot be expressed as 12x with integer x that also makes 5x an integer, because 209/12 is not an integer. Even if this were ignored, the implied difference between 5x and 12x would not match 133, so 209 fails both ratio and difference conditions.

Option C:
Option C is correct because it follows from solving the simple linear equation based on the difference of 7x. The pair (95, 228) satisfies both the ratio 5:12 and the difference 133, so 228 is the unique larger number that fits all parts of the problem.

Option D:
Option D, 247, would require x = 247/12 ≈ 20.58, making the smaller number 5x non-integer and leading to a different difference than 133. Therefore, 247 does not satisfy the structure imposed by the ratio 5:12 and the given difference.

Let the numbers be 7x and 8x. The difference between them is 8x − 7x = x, and we are told this difference equals 15. So x = 15. Substituting back, the numbers are 7 × 15 = 105 and 8 × 15 = 120. The larger number is therefore 120.

Option A:
Option A, 105, is the smaller of the two numbers obtained from the correct solution. It correctly fits the ratio but does not match the description “larger number” in the question. Choosing 105 would therefore misinterpret which quantity is being asked for.

Option B:
Option B is correct because it corresponds to the 8x term when x = 15, which is explicitly the larger number in the ratio 7:8. Verifying, the difference 120 − 105 is indeed 15, and the ratio 105:120 simplifies to 7:8. This confirms that 120 satisfies both the ratio and difference conditions.

Option C:
Option C, 135, when paired with 120 (to keep a difference of 15), yields a ratio 120:135 = 8:9, not 7:8. If we reversed the roles, 135 and 120 would differ by 15 but still not simplify to 7:8. Thus, 135 cannot be the larger number under the stated ratio.

Option D:
Option D, 140, would require the smaller number to be 125 to maintain a difference of 15. The ratio 125:140 reduces to 25:28, which is again not equal to 7:8. Therefore, 140 is incompatible with the conditions given in the question.