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. a) In a group of 500 students, 280 like bananas, 310 like apples, and 55 do not like both the fruits.

(i) Find the number of students who like both the fruits.
(ii) Find the number of students who like only one fruit.
(iii) Show the result in a Venn-diagram.​

User Grinn
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1 Answer

18 votes
18 votes

Answer:

(i) 145

(ii) 300

Explanation:

Given:

total students ... 500

like bananas ... 280

like apples ... 310

dislike fruits ... 55

(i) Find the number of students who like both fruits.

To find the number of students who like both fruits we first add students who like bananas and apples and then subtract students who like at least one fruit.

Students who like at least one of the fruits:

like fruit = total - dislike fruits

like fruit = 500 - 55 = 445

Students who like both fruits:

like both = (like bananas + like apples) - like fruit

like both = (280 + 310) - 445

like both = 145

(ii) Find the number of students who like only one fruit.

To find this we have to find how many students like ONLY bananas and ONLY apples.

like one fruit = like only apples + like only bananas

To find students who like only apples and like only bananas we subtract students who like both (calculated in (i)).

like only apples = like apples - like both = 310 - 145 = 165

like only bananas = like bananas - like both = 280 - 145 = 135

Therefore,

like one fruit = like only apples + like only bananas

like one fruit = 165 + 135

like one fruit = 300

(iii) Show the result in a Venn-diagram.

See attached picture.

. a) In a group of 500 students, 280 like bananas, 310 like apples, and 55 do not-example-1
User Vitor Durante
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