A school has 100 students and every student plays either cricket or football or both. The number of students who play cricket is twice the number of students who play football. Also, the number of students who play only cricket is three times the number of students who play only football. The number of students who play both cricket and football is, therefore:
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Answer:
n(u) = n(CuF)= 100
n(c) = 2n(F)
now,
no(c) = 3no(F)
or, n(c)-n(cnf) = 3n(f)-3n(cnf)
or 3n(f) - 2n(f) = 2n(cnf)
so, n(f) = 2n(cnf)
we know,
n(cuf) = n(c) + n(f) - n(cnf)
or 100 = 2n(f)+2n(cnf)-n(cnf)
or, 100 = 4n(cnf)+2n(cnf)-n(cnf)
so, 100 = 5n(cnf)
so, n(cnf) = 20
20 like both cricket and foot,