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If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take Physics & Chemistry and 38 take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is

Options

  1. A42
  2. B56
  3. C270
  4. D98

Correct answer

D. 98

Step-by-step solution

Let, M → Mathematics, P → Physics, C → Chemistry Given that total students = 200 n M = 120 , n P = 90 , n C = 60 n M ∩ P = 50 , n M ∩ C = 50 , n P ∩ C = 43 n M ∩ P ∩ C = 3 8 Required number of students taking exactly one subject is n M + n P + n C - 2 n M ∩ P - 2 n P ∩ C - 2 n M ∩ C + 3 n M ∩ P ∩ C = 120 + 90 + 60 - 2 50 - 2 50 - 2 43 + 3 38 = 98

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