English
Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9

If n(A ∪ B ∪ 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 - Mathematics

Advertisements
Advertisements

Question

If n(A ∪ B ∪ 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

Options

  • 10

  • 15

  • 25

  • 30

MCQ
Advertisements

Solution

15

Explanation;

Hint:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)

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

100 = 15x – 50

⇒ 150 = 15x

⇒ x = `150/15`

= 10

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Set Language - Exercise 1.7 [Page 37]

APPEARS IN

Samacheer Kalvi Mathematics [English] Class 9 TN Board
Chapter 1 Set Language
Exercise 1.7 | Q 16 | Page 37
Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×