In a joint family, 55% of members like Yogurt, and 55% of members like Ice cream. Then how much % of family members like both Yogurt and Ice cream

In a joint family, 55% of members like Yogurt, and 55% of members like Ice cream. Then how much % of family members like both Yogurt and Ice cream Correct Answer 10%

Given:

55% of members like Yogurt

55% of member like Ice cream

Formula Used:

Using set theory,

n(AUB) = n(A) + n(B) – n(AnB)

Where,

n(AUB) is total number of A union B

n(A) is number of A set

n(B) is number of B set

n(AnB) is number of A intersection B

Calculation:

In the above question,

Out of 100%,

n(A) = 55%

n(B) = 55%

Now by using formula,

n(AUB) = n(A) + n(B) – n(AnB)

⇒ 100 = 55 + 55 – n(AnB)

⇒ 100 = 110 – n(AnB)

⇒ n(AnB) = 110 – 100

⇒ n(AnB) = 10

∴ Out of total family members 10% like both Yogurt and Ice cream.

Out of 100%, 55% like Yogurt, 55% like Ice cream

⇒ (55 + 55) – 100

⇒ 110 – 100

⇒ 10

∴ Out of total family members 10% like both Yogurt and Ice cream.