Question

QUESTION FOR MODS N BRAINLY STARS NO SPAM In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple s well as orange juice. Find how many students were taking neither apple juice nor orange juice [ from chapter SETS]

Answer 1

“225” .

$\huge\bold{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• In a survey of 400 student's in a school .

• 100 were listed as taking Apple juice .

• 150 were listed as taking Orange juice.

• 75 were listed as taking both Apple as well as Orange juice .

TO FIND :-

• How many students were taking neither Apple nor Orange juice ?

CALCULATION :-

Let,

✍️ ‘T’ be the set of total students of the school in the survey .

✍️ ‘A’ be the set of students, who were taking Apple juice .

✍️ ‘O’ be the set of students, who were taking Orange juice .

According to the question,

• n (T) = 400

• n (A) = 100

• n (O) = 150

• $\underline\bold{n\:(A\:\cup\:O)\:=\:175\:}$

We have know that,

$\orange\bigstar\:\rm{\green{\boxed{n\:(A\:\cup\:O)\:=\:n\:(A)\:+\:n\:(O)\:-\:n\:(A\:\cap\:O)\:}}}$

$\rm{\implies\:n(A\:\cup\:O)\:=\:100\:+\:150\:-\:75\:}$

$\rm{\blue{\implies\:n(A\:\cup\:O)\:=\:175\:}}$

✍️ Number of students taking neither Apple nor Orange juice is,

• $\rm{\purple{n\:(\:\overline{A\:\cup\:O}\:)}}$

$\green\checkmark\:\mathcal{\red{\boxed{n\:(\:\overline{A\:\cup\:O}\:)\:=\:n(T)\:-\:n(A\:\cup\:O)\:}}}$

$\rm{\implies\:n\:(\:\overline{A\:\cup\:O}\:)\:=\:400\:-\:175\:}$

$\rm{\purple{\boxed{\blue{\implies\:n\:(\:\overline{A\:\cup\:O}\:)\:=\:225\:}}}}$

$\red\therefore$ $<font color=gray>$ There are 225 student's, who were taking neither Apple juice nor Orange juice .

Answer 2

Answer:

N(s) = 400

100 sᴛᴜᴅᴇɴᴛs ᴛᴀᴋᴇ ᴀᴘᴘʟᴇ ᴊᴜɪᴄᴇ,ɴ(A)=100

150 ᴛᴀᴋᴇ ᴏʀᴀɴɢᴇ ᴊᴜɪᴄᴇ,ɴ(ᴏ)=150

75sᴛᴜᴅᴇɴᴛ ᴛᴀᴋᴇ ʙᴏᴛʜ ᴀᴘᴘʟᴇ ᴀɴᴅ ᴏʀᴀɴɢᴇ ᴊᴜɪᴄᴇ, ɴ(A∩ᴏ) =75

Sᴏ,ɴ(A∪ᴏ)=ɴ(A)+ɴ(ᴏ)−ɴ(A∩ᴏ)

=100+150−75

=175

Nᴜᴍʙᴇʀ Oғ Sᴛᴜᴅᴇɴᴛs Tᴀᴋɪɴɢ Eɪᴛʜᴇʀ Aᴘᴘʟᴇ Oʀᴀɴɢᴇ

ᴊᴜɪᴄᴇ,

ɴ( A∪ᴏ )=ɴ(s)−ɴ(A∪ᴏ)

=400−175

=225

Step-by-step explanation:

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