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Directions for the questions: In a class, 30% of the students gave their names to participate in the NSS and 75% to participate in the NCC. Three students participate in neither of these two and six students wanted to participate in both. How many students are there in the class?Choices:- 60 75 80 100

Question

Directions for the questions: In a class, 30% of the students gave their names to participate in the NSS and 75% to participate in the NCC. Three students participate in neither of these two and six students wanted to participate in both. How many students are there in the class?Choices:- 60 75 80 100

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Solution

To solve this problem, we need to use the formula of the principle of inclusion and exclusion which states that for any two sets A and B, the size of their union is given by:

|A ∪ B| = |A| + |B| - |A ∩ B|

Where:

  • |A ∪ B| is the total number of students in the class,
  • |A| is the number of students who want to participate in NSS,
  • |B| is the number of students who want to participate in NCC,
  • |A ∩ B| is the number of students who want to participate in both NSS and NCC.

From the problem, we know that:

  • 30% of the students want to participate in NSS,
  • 75% of the students want to participate in NCC,
  • 6 students want to participate in both NSS and NCC,
  • 3 students do not want to participate in either.

Let's denote the total number of students in the class by x. Then we have:

0.30x + 0.75x - 6 = x - 3

Solving this equation for x gives:

x = 75

So, there are 75 students in the class. The correct answer is 75.

This problem has been solved

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