Let 1/x = a , 1/y = b , 1/z = c

The new equations are

a + b = 1/3 ----->1

a + c = 1/5 ------->2

b +c = 1/7 ------->3

By solving 2 and 3, a-b = 2/35 ---> 4

Solving for a , we get a= 41/210

Substitute a in equation 4 , we get value of b as 29/210

X/Y = 1/a * b = 29/210 * 210 /41 == 29/41

Ans : X/Y = 29/41