Question

There are 50 people at the city swim park today. Everyone in the park was wearing swim suits or sunglasses, some people had both. How many people had swim suits on but not sunglasses, if you know 38 have swim suits on and 25 have sunglasses?

1. 35.
2. 49.
3. 41.

Answer 1

Given :

There are 50 people at the city swim park today. Everyone in the park was wearing swim suits or sunglasses, some people had both.

38 have swim suits on and 25 have sunglasses.

To Find :

How many people had swim suits on but not sunglasses.

Solution :

Let, A refer swim suits and B refer sunglasses.

∞∪∩

A ∪ B = 50

A = 38

B = 25

We need to find, A - (A ∩ B) .

We know,

(A ∩ B) = A + B - (A ∪ B)

(A ∩ B) = 38 + 25 - 50

(A ∩ B) = 13

So, A - (A ∩ B) = 38 - 13 = 25

Therefore, number of people with swim suits on but not sunglasses are 25.