A group of persons, 55 enjoy going to the movies, 53 enjoy solving physics problems and 41 enjoy reading novels. Of these, 8 persons like all three activities, while 59 like only one of them. Then, how many persons like only two of the three activities?

A group of persons, 55 enjoy going to the movies, 53 enjoy solving physics problems and 41 enjoy reading novels. Of these, 8 persons like all three activities, while 59 like only one of them. Then, how many persons like only two of the three activities? Correct Answer 33

Given:

Person who enjoy going to movies = 55

Person who enjoy solving physics problems = 53

Person who enjoy reading novels = 41

Person who enjoy all three activities = 8

Person who like only one of them = 59

Concept:

Venn Diagram

Calculation:

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Given, X + Y + Z = 59

According to question –

⇒ X + a + 8 + b = 55

⇒ X + (a + b) = 47     ---- (i)

⇒ Y + a + c + 8 = 53

⇒ Y + (a + c) = 45      ----- (ii)

⇒ Z + (b + c + 8) = 41

⇒ Z + (b + c) = 33      ---- (iii)

Add (i) + (ii) + (iii), we get –

⇒ (X + Y + Z) + 2(a + b + c) = (47 + 45 + 33)

⇒ 59 + 2(a + b + c) = 125

⇒ 2(a + b + c) = 125 – 59

⇒ 2(a + b + c) = 66

⇒ a + b + c = 33

∴ Persons like only two of the three activities = 33