    Question

# In a sports fest, a school awarded 58 medals in athletics, 20 medals for indoor games and 25 medals for outdoor games. If these medals were bagged by a total of 78 students and only 5 students got medals for all the three activities, then the number of students who received medals for exactly two of the three activities is

A
30
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B
15
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C
20
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D
40
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Solution

## The correct option is B 15Let A, I, O be the set of students who bagged medals in athletics, indoor games and outdoor games respectively. It is given that n(A)=58, n(I)=20, n(O)=25, n(A∪I∪O)=78 and n(A∩I∩O)=5. Let x denotes the number of students who got medals in athletics and indoor games only, y denotes the number of students who got medals in indoor games and outdoor games only, z denotes the number of students who got medals in athletics and outdoor games only. This data can be represented in form of Venn Diagram as Now, n(A∪I∪O)=78⇒n(A)+n(I)+n(O)−n(A∩I)−n(I∩O)−n(A∩O)+n(A∩I∩O)=78⇒58+20+25−n(A∩I)−n(I∩O)−n(A∩O)+5=78⇒108−n(A∩I)−n(I∩O)−n(A∩O)=78⇒n(A∩I)+n(I∩O)+n(A∩O)=30⇒(x+5)+(y+5)+(z+5)=30⇒x+y+z=15 Therefore, required number of students is 15.  Suggest Corrections  0      Similar questions
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