Given that,
The ratio of Raju and Lalitha marbles $ = 4: 9$ (originally)
- The number of marbles Raju have $ = 4k$
- The number of marbles Lalitha have $ = 9k$
- Where $k$ is some constant.
Let Lalitha gave marbles to Raju be $x.$
So$,\dfrac{4k+x}{9k-x} = \dfrac{5}{6}$
$ \Rightarrow 6(4k+x) = 5(9k-x)$
$ \Rightarrow 24k + 6x = 45k – 5x$
$ \Rightarrow 11x = 21k$
$ \Rightarrow \boxed{ x = \left( \frac{21}{11} \right) k} $
$\therefore$ The fraction of Lalitha's original number of marbles given to Raju $ = \dfrac{x}{9k}$
$\qquad = \dfrac{ \left( \frac{21}{11} \right)k} {9k}$
$ \qquad = \frac{21}{9 \times 11}$
$\qquad = \frac {7}{33}$
Correct Answer $ : \text{B}$