Question

A survey shows that 84% of the Indians like grapes, whereas 45%
Ilke pineapple. What percentage of Indians like both grapes and
pineapple?
​

Answer 1

Answer:

29 % Indians

Detailed Explanation:

Given :

Total Percentage = n(U) = 100%

                                n(G) = 84%

                                n(P)  = 45%

*Note : u represents Union

           n represents Intersection

n(G u P) = n(G) + n(P) - n(G n P)

      100 = 84 + 45 = n(G n P)

n(G u P) = 29%

29% of the Indians like both Grapes and Pineapple

Hope The Answer was Helpful.

Answer 2

29% of the Indians like both grapes and pineapple

Given :

A survey shows that 84% of the Indians like grapes, whereas 45% Iike pineapple

To find :

The percentage of Indians like both grapes and pineapple

Solution :

Step 1 of 2 :

Write down the given data

Let ,

U = Set of all Indians

A = Set of Indians who like grapes.

B = Set of Indians who like pineapple

It is given that 84% of the Indians like grapes, whereas 45% Iike pineapple

Thus we get ,

n(A) = 84%

n(B) = 45%

n(U) = n(A ∪ B) = 100%

Step 2 of 2 :

Calculate the percentage of Indians like both grapes and pineapple

We know that ,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ 100% = 84% + 45% - n(A ∩ B)

⇒ n(A ∩ B) = 129% - 100%

⇒ n(A ∩ B) = 29%

Hence 29% of the Indians like both grapes and pineapple

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