Question

In a quiz competition out of 880
participants, 224 choose Mathematics
240 choose Science and 336 choose
Sports, 64 choose both Sports and
Science, 80 choose Mathematics and
Sports, 40 choose Mathematics and
Science and 24 choose all the three
subjects
96. The percentage of participants
who did not choose any subject is:
(1) 23.59
(2) 30.25
(3) 37.46
(4) 27.27
97. Of those participating, the
percentage who choose only one
subject is :
(1) 60
(2) More than 60
(3) Less than 60
(4) More than 75​

Answer 1

Answer: 96) (4) 27.27

97) (3) Less than 60

Step-by-step explanation:

Let mathematics M

Science S

Sports T

Given : n(M)=224 , n(S)= 240 , n(T)= 336

n(M∩S)= 40 , n(M∩T)=80 n(S∩T)= 64

n(M∩S∩T)= 24

Therefore from the diagram

n(M∪S∪T) = 128+ 16+160+56+24+40+216= 640

Now total students = 880

Students who did not participate in any course = 880 - 640= 240

96)

Percentage = $\dfrac{240}{880} \times 100 = 27.27\%$

(4) is correct option

97)

Participants choose  only one subject = 128+160+216= 504

Percentage = $\dfrac{504}{880} \times 100 = 57.27\%$

(3) is correct option

Answer 2

Answer:

Let mathematics M

Science S

Sports T

Given : n(M)=224 , n(S)= 240 , n(T)= 336

n(M∩S)= 40 , n(M∩T)=80 n(S∩T)= 64

n(M∩S∩T)= 24

Therefore from the diagram

n(M∪S∪T) = 128+ 16+160+56+24+40+216= 640

Now total students = 880

Students who did not participate in any course = 880 - 640= 240

96)

Percentage = \dfrac{240}{880} \times 100 = 27.27\%

880

240

×100=27.27%

(4) is correct option

97)

Participants choose only one subject = 128+160+216= 504

Percentage = \dfrac{504}{880} \times 100 = 57.27\%

880

504

×100=57.27%

(3) is correct option