Combining work rates in ratio form – UGC NET Question

If A finishes the work in 12 days, A’s one-day work is 1/12. If B finishes in 18 days, B’s one-day work is 1/18. The ratio of A’s work to B’s work in one day is (1/12):(1/18) = 18:12, which simplifies to 3:2. Hence, the required ratio is 3:2.

Option A:
Option A, 2:3, is the inverse of the correct ratio. It would imply that B does more work per day than A, suggesting that B is faster, which contradicts the given completion times where A finishes in fewer days.

Option B:
Option B, 4:3, does not result from the fraction 1/12 divided by 1/18. If we equate 4:3 to 18:12, we see that 18:12 simplifies to 3:2, not 4:3. Thus 4:3 cannot represent the actual comparison of their daily work.

Option C:
Option C, 5:4, appears as a plausible ratio but has no basis in the calculations from 12 and 18 days. When we compute the exact fractions, 1/12 and 1/18, they do not simplify in a way that yields 5:4. Therefore, 5:4 is inconsistent with the numerical data.

Option D:
Option D is correct because it reflects the fact that A’s daily work is greater than B’s in the precise proportion 3:2. This means that for every 3 units of work A does in a day, B does 2 units, matching the relative speeds implied by their completion times.