Squeezy fractions

Suppose $a, b$ are positive integers satisfying:

$\frac {27}{197} < \frac {a}{b} < \frac {41}{299}$ .

Let $B$ (a positive integer) be the minimum value of $b$ such that there exists a positive integer value of $a$ , say $A$ , such that this equation is satisfied.

Let D ( a positive integer) be the minimum value of d such that there exists a positive integer value of $c$ , satisfying the following inequality:

$\frac {27}{197} < \frac {c}{d} < \frac {A}{B}$ .

Evaluate $B+D$ .