The average weight of the boys in a class is 69.3 kg and that of the girls in the same class is 59.4 kg. If the average weight of all the boys and girls in the class is 63.8 kg, then the percentage of the number of boys in the class is:

Let B be the number of Boys, G be number of girls 

$$ \dfrac {total   weight   of   boys}  {number  of   boys} $$= Any weight of boys 

total weight of boys = (69.3)B 

Similarly total weight of girls = (59.4) G

total weight of class = 69.3 B + 59.4 G 

Any weight of class = $$\dfrac{total   weight   of   class}{total   Boys  + Girls} $$ 

$$\Rightarrow 63.8 = \dfrac{ 63.3 B + 59.4 G} {B + G} $$ 

$$\Rightarrow 63.8 B + 63.8 G = 69.3 B + 59.4 G $$

$$\Rightarrow 4.4 G = 5.5 B $$

$$\Rightarrow G = \dfrac {5}{4} B $$

% of Boys in class = $$\dfrac{B}{B+G} \times 100 $$

$$\Rightarrow \dfrac{B}{B + \dfrac{5}{4}B} \times 100 $$

$$\Rightarrow \dfrac{B}{B+ \dfrac{9}{4}B} \times 100 $$ 

$$\Rightarrow \dfrac{4}{9} \times 100 $$

$$\Rightarrow \dfrac {400}{9} $$

$$\Rightarrow 44 \dfrac{4}{9} $$ Ans