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Raju and Lalitha originally had marbles in the ratio $4:9$. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became $5:6$. What fraction of her original number of marbles was given by Lalitha to Raju?

1. $1/4$
2. $7/33$
3. $1/5$
4. $6/19$

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 $: \text{B}$

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