Question

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?​

Answer 1

Answer: 70

Step-by-step explanation:

Answer 2

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