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…

Correct Option

Let x represent the total number of boys in the class.

It is given that 18 very tall boys constitute three-fourths of the total boys. Therefore:

$$18 = \frac{3}{4} \times x$$18=43​×x

∴ Solving for x:

$$x = \frac{18 \times 4}{3} = 24$$x=318×4​=24

Thus, there are 24 boys in the class.

Next, let y represent the total number of students in the class.

It is stated that the total number of boys is two-thirds of the total number of students. Therefore:

$$24 = \frac{2}{3}y$$24=32​y

∴ Solving for y:

$$y = \frac{24 \times 3}{2} = 36$$y=224×3​=36

Thus, there are 36 students in total in the class.

The number of girls in the class is determined by subtracting the total number of boys from the total number of students:

Number of girls = y - x = 36 - 24 = 12.

Incorrect Options

The precise calculation based on the given proportions yields 12 girls. The other options are incorrect for the following reasons:

• Option 1 (6): This value does not align with the derived number of girls and would result from a misapplication of the given fractional relationships.
• Option 3 (18): This figure represents the number of very tall boys, not the total number of girls in the class.
• Option 4 (21): This value is not obtained through the correct sequential application of the proportions provided in the problem statement.