Question

In a class, there are 18 boys who are over 160cm tall. 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?
A) 6
B) 12
C) 18
D) 24

Answer 1

- Hint: Firstly, find total number boys using the given fractions and then find the total number of students. After this, find the difference between total students and boys which will give the number of girls students in the class. We find that the total number of boys that is X which is equal to 24 and the total number of students that is Y which is equal to 36. Total number of girls is equal to Y-X=12.

Complete step-by-step solution:
Firstly, let the total number of boys and students
Let the total numbers of boys = x
And the total number of students = y
As given in the question
There are 18 boys who are over 160cm tall and these constitutes three-fourths of the boys
The number of boys=$\dfrac{3}{4}x$
So, we calculate the total number of boys=$\dfrac{3}{4}x$$ = 18$
Then total number of boys, $x = 24$
The total number of students =$\dfrac{2}{3}$y
So, we calculate the total number of students=$\dfrac{2}{3}y = 24$
Then total number of students, y = 36
So, the total numbers of girls in the class=total number of students-total number of boys
The total number of girls = total number of boys(x)-total number of students(Y)
Then $36 - 24 = 12$

Therefore, the total number of girls in the class is 12. So, the correct answer is option B.

Note:
In these types of questions assume the unknown quantities and equate it with the relations that are given in the question. As in question conditions are given from these conditions: calculate total number of boys and total number of students.