In a survey of 1000 fruit eaters who like to east one fruit among people, mango and grapes; 400 do not like grape, 380 do not like mango and 542 do not like apple, 294 like both mango and apple, 277 like both grape and mango and 120 like both grape and apple
How many people like only grapes.
a. 281
b. 107
c. 216
d. 207
e. 210
Answers
216 people likes only grap es
Step-by-step explanation:
Total = 1000
do not like gra pe = 400
Like grap es G = 600
do not like mango = 380
Like Mango M = 620
do not like apple = 542
like Apples A = 458
like both mango and apple M ∩ A = 294
like both mango and Grap es M ∩ G = 277
like both apple and Grap es A ∩ G = 120
M ∩ A ∩ G = ?
Total = G + M + A - M ∩ A - M ∩ G - A ∩ G + M ∩ A ∩ G
=> 1000 = 600 + 620 + 458 - 294 - 277 - 120 + M ∩ A ∩ G
=> M ∩ A ∩ G = 13
Likes only grap es = G - M ∩ G - A ∩ G + M ∩ A ∩ G
= 600 - 277 - 120 + 13
= 216
216 people likes only grap es
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Given :-
- Survey of 1000 fruit eaters
- 400 do not like grape
- 380 do not like mango
- 542 do not like apple,
- 294 like both mango and apple,
- 277 like both grapes and apple.
- 120 like both grape and apple
To Find :-
- how many people like exactly one fruit
Solution:-
Total = 1000
do not like grape = 400
Like grapes G = 600
do not like mango = 380
Like Mango M = 620
do not like apple = 542
like Apples A = 458
like both mango and apple M ∩ A = 294
like both mango and Grapes M ∩ G = 277
like both apple and Grapes A ∩ G = 120
M ∩ A ∩ G = ?
Total = G + M + A - M ∩ A - M ∩ G - A ∩ G + M ∩ A ∩ G
=> 1000 = 600 + 620 + 458 - 294 - 277 - 120 + M ∩ A ∩ G
=> M ∩ A ∩ G = 13
Likes only grapes = G - M ∩ G - A ∩ G + M ∩ A ∩ G
= 600 - 277 - 120 + 13
= 216