Equal subtraction changing a ratio – UGC NET Question

Let the numbers be 5x and 8x. After subtracting 20 from each, they become 5x − 20 and 8x − 20, with ratio 3:5. So (5x − 20)/(8x − 20) = 3/5. Cross multiplying gives 5(5x − 20) = 3(8x − 20), which simplifies to 25x − 100 = 24x − 60 and hence x = 40. The original numbers are therefore 200 and 320, so the larger is 320.

Option A:
Option A, 200, is the smaller original number when x = 40. If we took 200 as the larger, it would contradict the initial ratio 5:8, in which 8x must exceed 5x. Substituting 200 as the larger in the equations would also fail to reproduce the ratio 3:5 after subtraction.

Option B:
Option B, 240, does not correspond to either 5x or 8x for the solved value x = 40. If we attempted to solve using 240 as one of the numbers, the resulting x would not satisfy the transformed ratio condition. Hence 240 is inconsistent with the problem’s constraints.

Option C:
Option C, 280, again fails to match the form 5x or 8x with x = 40 and does not produce the stated ratio 3:5 after subtracting 20 from both numbers. Any attempt to fit 280 into the ratio structure leads to contradictions with the proportional relationship.

Option D:
Option D is correct because 320 equals 8 × 40, matching the larger term in the original ratio 5:8. With numbers 200 and 320, subtracting 20 gives 180 and 300, and 180:300 simplifies to 3:5. This verifies that 320 is the correct larger original number.