people who eat mangoes guavas and bananas are 40 ,50 and 60 respectively.10 people eat all the three f
ruits and 70 people eat exactly 1 fruit how many people eat exactly two fruits?
Answers
Answer: 70
Step-by-step explanation:
Given:
No. Of people eating mangoes = M = 40
No. Of people eating guavas = G = 50
No. Of people eating bananas = B = 60
10 people eat all the three f ruits and 70 people eat exactly 1 fruit
To Find:
How many people eat exactly two fruits?
Solution:
Let x , y and z be number of people who only eat Mangoes , guavas and bananas, respectively.
Therefore, x + y+ z = 70;
Let a be the number of people who eat Mangoes and guavas.
Let b be the number of people who eat Mangoes and bananas
Let c be the number of people who eat bananas and guavas.
Let d be number of people who eat all 3, d = 10
From the venn diagram,
- M - ( a + b ) + d = x;
- G - ( a + c ) + d = y;
- B - ( b + c ) + d = z;
Therefore,
- M + d - x = a + b ;
- G + d - y = a + c ;
- B + d - z = b + c ;
Adding all three,
- M + G + B +3d - ( x + y + z ) = 2 ( a + b + c )
- 40 + 50 + 60 + 30 - 70 = 2 ( a + b + c )
- a + b + c = 55 .
Now, We can see from the venn diagram that,
people who eat only 2 fruits is
- Mangoes and guavas only : a - d ,
- Mangoes and bananas only : b - d,
- bananas and guavas only : c -d
Therefore number of people who only eat 2 fruits is:
- a - d + b - d + c -d = 55 - 30 = 25
The number of people who eat exactly two fruits is 25
