Question

In a survey, it was found that 55% go for jogging, 50% do yoga, 42% do aerobics, 28% do jogging and yoga, 20% do yoga and aerobics, 12% go for jogging and aerobics and 10% do all three. If each one of them go for atleast one of these, then what percentage do exactly one exercise? (1) 40% (2) 49% (3) 57% (4) 59% solve without vein daigram

Answer 1

Answer:

percentage which do exactly one event is 59%

Step-by-step explanation:

Events are Jogging, Yoga, Aerobics,  

Let us represent them with letters J, Y and A respectively.  

n(J) = 55, n(Y) = 50, n(A) = 42

n(J ∩ Y) = 28

n(Y ∩ A) = 20

n(J ∩ A) = 12

n(J ∩ Y ∩ A) = 10

n(Only J) = n(J) – n(J ∩ Y) – n(J ∩ A) + n(J ∩ Y ∩ A)

n(ONLY J) = 55 – 28 – 12 + 10 = 29

n(Only Y) = n(Y) – n(J ∩ Y) – n(Y ∩ A) + n(J ∩ Y ∩ A) = 50 – 28 – 20 + 10 = 12

n(Only A) = n(A) – n(A ∩ Y) – n(J ∩ A) + n(J ∩ Y ∩ A) = 42 – 20 -12 +10 = 18

Hence percentage which do exactly one event is (29 + 12 + 18) = 59%