Two numbers are in the ratio of 5 : 6. If 8 is subtracted from them, they become in the ratio of 4 : 5. The numbers are:

Let the numbers be 5k and 6k. After subtracting 8 from each, the ratio becomes 4:5, so (5k - 8)/(6k - 8) = 4/5. Cross-multiplying gives 25k - 40 = 24k - 32, so k = 8. The numbers are 40 and 48. Check: 32 : 40 = 4 : 5. So A is correct.

Why the others fail:

• B (15, 16): The original ratio is 15 : 16, not 5 : 6.
• C (25, 30): The ratio 5 : 6 holds, but subtracting 8 gives 17 : 22, not 4 : 5.
• D (15, 18): The ratio 5 : 6 holds, but subtracting 8 gives 7 : 10, not 4 : 5.

The core concept is solving a ratio problem with a constant shift: write both numbers as multiples of a common unknown, then apply the second condition to form a linear equation. The same method works for age and partnership problems in Quantitative Aptitude, which are common in Prelims and useful in Mains data-based reasoning.

Trap: Options C and D satisfy the first condition, so a candidate who checks only the original ratio may pick one of them. Always verify both conditions.