Question 1197952
<font color=black size=3>
b = number of boys
g = number of girls
b+g = number of pupils


3/4 of the [number of] boys = 1/3 of the [number of] girls
(3/4)b = (1/3)g
12*(3/4)b = 12*(1/3)g
9b = 4g
9b/g = 4
b/g = 4/9
g/b = 9/4


k = fraction of the pupils that are boys
(number of boys)/(number of pupils) = k
b/(b+g) = k
(b+g)/b = 1/k
b/b + g/b = 1/k
1 + g/b = 1/k
1 + 9/4 = 1/k  .... plug in g/b = 9/4
4/4 + 9/4 = 1/k
(4+9)/4 = 1/k
13/4 = 1/k
4/13 = k
k = 4/13


Answer: <font color=red>4/13</font> of the pupils are boys.


Side note: 9/13 is the fraction of girls (since 4/13+9/13 = 1)
</font>