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In a farewell party, 35% persons like soft drink and 55% persons like hard drink. If 10% of persons like both the drink, then what per cent of persons drink neither soft nor hard drink ?

In a farewell party, 35% persons like soft drink and 55% persons like hard drink. If 10% of persons like both the drink, then what per cent of persons drink neither soft nor hard drink ? Correct Answer 20%

Given:

35% persons like soft drink and 55% persons like hard drink. If 10% of persons like both the drink.

Concept used:

(x U y) = n(x) + n(y) – n(x ∩ y)

Calculation:

Let x and y represent the persons like soft and hard drink respectively

Let A be the percentage of persons drink neither soft and hard drink

According to the question,

35% persons like soft drink

⇒ n(x) = 35%

55% persons like hard drink

⇒ n(y) = 55%

10% persons like both soft and hard drink

⇒ n(x ∩ y) = 10

Now,

n(x) + n(y) + A  – n(x ∩ y) = 100

⇒ 35 + 55 + A  – 10 = 100

⇒ A = 110  – 90

⇒ A = 20

∴ 20% persons drink neither soft and hard drink.

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