Answer: 3 and 4.
Solution: Since Ram knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Krishna (who knows x × y) knew that Ram didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Krishna doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 × 4, 12 = 6 × 2). At this point Ram knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.
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