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 C38 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:
(12×100)+(13×300)=50+100=150
Now, we divide the number of hostel dwellers by the total number of students to find the required fraction: