$3\leq X\leq 5 ----- eqn. 1$
Now using multiplicative inverse property on Y
When a and b are both positive or both negative: (Direction of inequality changes)
If a < b then 1/a > 1/b
If a > b then 1/a < 1/b
But when either a or b is negative (not both) the direction stays the same:
If a < b then 1/a < 1/b
If a > b then 1/a > 1/b
$\therefore Y becomes \frac{1}{11}\leq \frac{1}{Y}\leq \frac{1}{8} ------ eqn. 2$
Now multiplying eqn.1 and eqn. 2 we get
$\frac{3}{11}\leq \frac{X}{Y}\leq \frac{5}{8}$
Hence option B is correct.