In a class there are 18 boys who are over 160 cm tall. If these boys constitute three-fourths of the boys and the total number of boys is two-third of the number of students in the class, then what is the number of girls in the class?

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Q: 139 (IAS/2000)
In a class there are 18 boys who are over 160 cm tall. If these boys constitute three-fourths of the boys and the total number of boys is two-third of the number of students in the class, then what is the number of girls in the class?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,8,4,1,8,2,1

keywords: 

{'students': [0, 1, 1, 1], 'fourths': [0, 1, 0, 0], 'boys': [0, 1, 5, 11], 'girls': [0, 2, 3, 10], 'total number': [0, 0, 3, 0], 'number': [0, 0, 0, 2], 'class': [4, 1, 4, 15], 'third': [2, 1, 3, 6]}

Let`s assume the total number of boys in the class as `B` and the total number of students in the class as `S`.

According to the given information:

1. 18 boys are over 160 cm tall, which constitutes three-fourths of the boys. So, (3/4)B = 18.

Multiplying both sides by (4/3) gives B = 24.

2. The total number of boys is two-thirds of the total number of students. So, B = (2/3)S.

Substituting the value of B as 24, we get 24 = (2/3)S.

Multiplying both sides by (3/2) gives S = 36.

Now, to find the number of girls, we subtract the number of boys from the total number of students:

Number of girls = S - B = 36 - 24 = 12.

Therefore, the number of girls in the class is 12.