Jambmaths question:
In a class of 40 students,each student offers at least one of physics and chemistry. If the number of students that offers physics is 3 times the number that offer both subject and the number that offer chemistry is twice the number that offer physics. Find the number of students that offers physics only
Option A:
15
Option B:
25
Option C:
5
Option D:
10
Jamb Maths Solution:
$\begin{align} & n(\xi )=40 \\ & n(P)=3x \\ & n(P\cap C)=x \\ & n(C)=2\left[ n(P) \right] \\ & n(C)=2(3x)=6x \\ & n(P\cup C)=n(\xi )=40 \\ & n(P\cup C)=n(P)+n(C)-n(P\cap C) \\ & 40=3x+6x-x \\ & 40=8x \\ & x=5 \\ & n(P)=3\times 5=15 \\ & n(P\cap {{C}^{1}})=n(P)-n(P\cap C) \\ & n(P\cap {{C}^{1}})=15-5 \\ & n(P\cap {{C}^{1}})=10 \\\end{align}$
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