Question : Directions: In a class of 120 students, 100 students participate in either Golf or Skating, or both. Among them, a total of 60 students participate in Golf. A total of 56 students participate in Skating. How many students participate only in Skating?
Option 1: 40
Option 2: 16
Option 3: 44
Option 4: 36
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Correct Answer: 40
Solution : In the Venn diagram representation, the G circle shows the number of players playing golf, and the S circle shows the number of players playing skating. The common area shows the players playing both games. The outside area shows players playing neither of the games.
Number of players playing neither of the games = 120 – 100 = 20
Let the number of players playing both games be x.
A total of 60 students participate in golf.
So, the number of players playing only Golf = 60 – x
A total of 56 students participate in skating.
So, the number of players playing only skating = 56 – x
The total number of players playing golf and skating = 100
So, (60 – x) + (56 – x) + x = 100
⇒ 116 – 2x + x = 100
⇒ 116 – x = 100
⇒ x = 116 – 100
⇒ x = 16
So, the number of players playing only skating is (56 – 16) = 40. Hence, the
first option
is correct.
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