Marks ratio from percentages – UGC NET Question

A’s marks are 72% of 750, which is (72/100) × 750 = 540. B’s marks are 84% of 750, which is (84/100) × 750 = 630. The ratio A:B is 540:630. Dividing both numbers by 90 gives 6:7. Hence, the ratio of A’s marks to B’s marks is 6:7.

Option A:
Option A is correct because it simplifies the raw scores 540 and 630 using their highest common factor. Dividing both by 90 yields exactly 6:7, which preserves the proportion while using smaller, more convenient numbers. This process directly matches standard ratio reduction techniques.

Option B:
Option B, 7:8, might be guessed from the numerical percentages 72% and 84%, but the percentages cannot be compared directly without considering the total marks. When we compute the actual scores, the ratio 540:630 does not simplify to 7:8, so this option is incorrect.

Option C:
Option C, 4:5, would require A’s marks to be four-fifths of B’s marks. If B had 630, then A would need to have 504, not 540. Since A’s actual score is higher than 504, the ratio 4:5 understates A’s relative performance and does not match the data.

Option D:
Option D, 9:10, suggests a nearly equal performance, but if we scale 540 and 630 to 9 and 10, we find that 540 × 10 ≠ 630 × 9. This shows that 9:10 is not equivalent to 540:630, so it cannot represent their actual mark ratio.