Question

In a class there are 18 boys who are over 160 cm 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?

Answer 1

Hint: Here, assume that the number of boys students is x and the total number of students is y. Compare three-fourth of x equal to 18 and the value of x. Similarly find the value of y using a given statement. Then subtract the number of boys from the total number of students.

Complete step-by-step answer:
Given: Total number of boys who are over tall = 160 cm
Let the number of boys be X.
Then according to the question, $\dfrac{3}{4} \times x$ = 18
 x = $18 \times \dfrac{4}{3}$
 ⇒ x = 24
So, the number of boys is 24.
Let the total number of students is Y.
Then according to the question,
$\dfrac{2}{3} \times y$ = 24 ⇒ Y =$24 \times \dfrac{3}{2}$
 ⇒ Y = 36
So, the number of girls in class = Y − X = 36 – 24 = 12

Therefore, the number of girls = 12 and the number of boys = 24.

Note: let the number of boys when in question does not specify some information for finding the number of girls. if you want to find girls then always deduct from total number of boys and total number of students because student has both number of girls and number of boys.
Alternatively, we can ask this question by assuming the total number of students as 100. Find the numbers of boys and girls with respect to the total 100 students. Lastly, use a unitary method to find the number of girls. But be careful while solving using the unitary method. 100 students is just an assumption to compare the number of boys and girls, never leave the answer without using a unitary method.