The number of girls in XI in the school S3 is approximately ______% of the number of boys in IX in the school S2.

The relevant data from the table:

School	Class	Total Students	% of Boys	% of Girls
S3	XI	100	65%	$100 - 65 = 35\%$
S2	IX	150	30%	—

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The number of girls in School S3 (Class XI):

$\text{Girls}$

$= \text{Total Students} \times (\% \text{ Girls})$

$= 100 \times 35\%$

$= 100 \times 0.35$

$= 35$

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The number of boys in School S2 (Class IX):

$\text{Boys}$

$= \text{Total Students} \times (\% \text{ Boys})$

$= 150 \times 30\%$

$= 150 \times 0.30$

$= 45$

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The percentage that the number of girls in S3 (Class XI) represents of the number of boys in S2 (Class IX):

$\text{Percentage}$

$= \left( \frac{\text{Girls (S3, XI)}}{\text{Boys (S2, IX)}} \right) \times 100$

$= \left( \frac{35}{45} \right) \times 100$

$= \frac{7}{9} \times 100$

$\approx 77.78\%$

Therefore, the answer is 77.78 (Option 3).