Finding numbers from ratio and difference – UGC NET Question

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.