$3$ . There are only chicken and fish as non-veg items in a party. In a group of $200$ non-veg people, $80$ like only chicken and $60$ like only fish. If the number of people who do not like any of the two non-veg items is double of the number of people who like both items, answer the following questions. $\newline$ (a) If the sets of people who like chicken and fish are represent by $\mathrm{C}$ and $\mathrm{F}$ respectively, what does $\mathrm{n}(\mathrm{C} \Delta \mathrm{F})$ mean? $\newline$ $[1 \mathrm{~K}]$ $\newline$ (b) Illustrate the above information in a Venn-diagram. $\newline$ $[1 \mathrm{U}]$ $\newline$ (c) Find the number of people who like at least one of the items. $\newline$ $[3 \mathrm{~A}]$ $\newline$ (d) How many people do not like chicken at all in each $100$ people? $\newline$ [ $1$ HA]

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3

. There are only chicken and fish as non-veg items in a party. In a group of

200

non-veg people,

80

like only chicken and

60

like only fish. If the number of people who do not like any of the two non-veg items is double of the number of people who like both items, answer the following questions.

\newline

(a) If the sets of people who like chicken and fish are represent by

\mathrm{C}

and

\mathrm{F}

respectively, what does

\mathrm{n}(\mathrm{C} \Delta \mathrm{F})

mean?

\newline

[1 \mathrm{~K}]

\newline

(b) Illustrate the above information in a Venn-diagram.

\newline

[1 \mathrm{U}]

\newline

\newline

[3 \mathrm{~A}]

\newline

(d) How many people do not like chicken at all in each

100

people?

\newline

[

1

HA]

Define $n(C\Delta F)$ : Step $1$ : Define $n(C\Delta F)$ in the context of the problem. $\newline$ $n(C\Delta F)$ represents the number of people who like either chicken or fish, but not both.
Draw Venn diagram: Step $2$ : Draw a Venn diagram. $\newline$ Draw two overlapping circles, one for chicken $C$ and one for fish $F$ . Label the only chicken area as $80$ , only fish as $60$ , and the intersection (both) as $x$ . The outside (neither) is $2x$ .
Calculate total people: Step $3$ : Calculate the total number of people who like both chicken and fish. $\newline$ Using the information that the number of people who do not like any of the two items is double the number of people who like both, we have: $\newline$ Total people = $200$ $\newline$ People who like neither = $2x$ $\newline$ People who like both = $x$ $\newline$ Equation: $80$ (only chicken) + $60$ (only fish) + $x$ (both) + $2x$ (neither) = $200$ $\newline$ $140 + 3x = 200$ $\newline$ $3x = 60$ $\newline$ $x = $20$
Find people like at least one: Step $4$: Find the number of people who like at least one of the items.$\newline$People who like at least one $=$ Total people $-$ People who like neither$\newline$$= 200 - 2x$$\newline$$= 200 - 40$$\newline$$= 160$
Calculate people not like chicken: Step $5$: Calculate how many people do not like chicken at all per $100$ people.$\newline$People who do not like chicken $=$ People who like only fish $+$ People who like neither$\newline$$= 60 + 40$$\newline$$= 100$$\newline$Percentage per $100$ people $= (100 / 200) * 100$$\newline$$= 50\%$