In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?

The correct option is 12.

Let's break down the problem step-by-step to find the number of girls in the class.

Step 1: Find the total number of boys in the class.
We are given that there are 18 very tall boys, and they constitute three-fourths (3/4) of the total number of boys in the class.
Let the total number of boys be represented by $B$.
According to the problem:

$\frac{3}{4}\times B=18$
To find $B$, we multiply both sides of the equation by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$:

$B=18\times \frac{4}{3}$
$B=6\times 4$
$B=24$
So, the total number of boys in the class is 24.

Step 2: Find the total number of students in the class.
We are told that the total number of boys is two-thirds (2/3) of the total number of students in the class.
Let the total number of students in the class be represented by $S$.
According to the problem:

$\frac{2}{3}\times S=B$
Substituting the value of $B=24$ into the equation:

$\frac{2}{3}\times S=24$
To find $S$, we multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$:

$S=24\times \frac{3}{2}$
$S=12\times 3$
$S=36$
So, the total number of students in the class is 36.

Step 3: Calculate the number of girls in the class.
The number of girls is the difference between the total number of students and the total number of boys.

$\text{Number of girls}=S-B$
$\text{Number of girls}=36-24$
$\text{Number of girls}=12$
Therefore, the number of girls in the class is 12.