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In a village 85% of the people speak Malayalam, 40% speak English and 20% speak Tamil. 32% speak Malayalam and English, 13% speak Malayalam and Tamil, and 10% speak English and Tamil. What is the percentage of people who can speak all three languages in the village?

In a village 85% of the people speak Malayalam, 40% speak English and 20% speak Tamil. 32% speak Malayalam and English, 13% speak Malayalam and Tamil, and 10% speak English and Tamil. What is the percentage of people who can speak all three languages in the village? Correct Answer 10%

GIVEN :

People who speak Malayalam = 85%

People who speak English = 40%

People who speak Tamil = 20%

People who speak Malayalam and English = 32%

People who speak Malayalam and Tamil = 13%

People who speak English and Tamil = 10%

 

CONCEPT :

Venn Diagram.

 

CALCULATION :

Let x be the percentage of people who speak all three languages in the village.

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From the above venn Diagram, we have

⇒ 100 = 40 + x + 32 – x + x + 13 – x + 10 – x – 2 + x – 3 + x

⇒ 100 = 40 + 32 + 13 + 10 - 2 – 3 + x

⇒ 100 = 95 – 5 + x

⇒ 100 = 90 + x

⇒ x = 100 - 90

⇒ 10%

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