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Question

Half the girls and one-third of the boys of a college reside in the hostel. What fractional part of the student body is hostel dwellers if the total number of girls in the college is 100 and is 114 of the total strength?


A
58
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B
78
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C
38
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D
18
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Solution

The correct option is C $$\dfrac{3}{8}$$
It is given that the total number of students in college is $$400$$ and the number of girls is $$100$$. Therefore, the number of boys in the college is

$$400-100=300$$.

Also it is given that half the girls and one-third of the boys of college reside in the hostel, therefore, the number of hostel dwellers are as follows:

$$\left( \dfrac { 1 }{ 2 } \times 100 \right) +\left( \dfrac { 1 }{ 3 } \times 300 \right) =50+100=150$$

Now, we divide the number of hostel dwellers by the total number of students to find the required fraction:

$$\dfrac { 150 }{ 400 } =\dfrac { 3 }{ 8 }$$ 

Hence, $$\dfrac { 3 }{ 8 }$$ of the student body is hostel dwellers.

Mathematics

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