We can add all the fractions and get,
$x + y = 3\, \dfrac{1}{3} + 4\, \dfrac{1}{5} + 5\, \dfrac{1}{7} + 7\, \dfrac{1}{2} + 5\, \dfrac{3}{7} - 4\, \dfrac{1}{5} - 5\, \dfrac{1}{7} - 7\, \dfrac{1}{2}$
$\implies x + y = 3\, \dfrac{1}{3} + 5\, \dfrac{3}{7}$
$\implies x + y = \dfrac{184}{21}.$
So, the correct answer is $(A).$