You can solve this question by choosing numbers.First, you can simplify 1/x+1/y as x+y/xy.
Case I : x=1, y=1. Quantity A would be 1+1/1 = 2. Quantity B would be 1 * 1 / 1+1 = 1/2. Here, Quantity A is greater.
Case II : x=3, y=4. Quantity A would be 3+4/3 * 4 = 7/12. Quantity B would be 3 * 4 / 3+4 = 12/7. Quantity B is greater.
Hence, answer is D.