Question

If n (A U B U C )= 100, n ( A ) = 4x, n ( B ) = 6x, n ( C ) = 5x, n (A ∩B )= 20, n (B ∩ C)= 15, n (A ∩ C)=25 and n (A ∩ B ∩C) = 10 , then the value of x is ______

Answer 1

Answer:

100=4x+6x+5x-20-15-25+10

=15x-50

15x=150

x=10

Answer 2

The value of x = 10

Given: n(AUBUC)= 100

n(A) = 4x, n(B) = 6x, n(C) = 5x

n(A∩B) =20,  n(B∩C) = 15,  n(A∩C)=25 and n(A∩B∩C) = 10

To find: The value of x

Solution: If A, B and C are 3 sets of elements then the formula for number of elements in A, B and C is given by

n(AUBUC) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩ C)  

Now substitute given values in above formula

⇒ 100 = 4x + 6x + 5x - 20 - 15 - 25 + 10

⇒ 100 = 15x - 60 + 10

⇒ 100 = 15x - 50

⇒ 100 + 50 = 15x

⇒ 150 = 15x

⇒ $x = \frac{150}{15}$ = 10

The value of x = 10

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