Question

2. In a town 85% of the people speak Tagalog, 40% speak Ilocano and 20% speak Bisaya. Also 32% speak Tagalog and Ilocano, 13% speak Tagalog and Bisaya, and 10% speak English and Hindi, find the percentage of people who can speak all the three languages.

Answer 1

Answer:

45℅

Step-by-step explanation:

32℅ Tangalog+IIocano

13℅ Tangalog+ Bisaya

32%+13%=45%

Answer 2

Correct Question

In a town 85% of the people speak Tagalog, 40% speak Ilocano and 20% speak Bisaya. Also, 32% speak Tagalog and Ilocano, 13% speak Tagalog and Bisaya, and 10% speak Ilocano and Bisaya, find the percentage of people who can speak all three languages.

Answer

Hence, 10% of people speak all 3 languages.

Given

• 85% of the people speak Tagalog
• 40% speak Ilocano
• 20% speak Bisaya
• 32% speak Tagalog and Ilocano
• 13% speak Tagalog and Bisaya
• 10% speak Ilocano and Bisaya

To Find

The percentage of people who can speak all three languages.

Solution

Let

• X be the people who speak Tagalog
• Y be the people who speak Ilocano
• Z be the people who speak Bisaya.

According to the problem

• (X) = 85% = 85/100
• (Y) = 40% = 40/100
• (Z) = 20% = 20/100
• (X∩Y) = 32% = 32/200
• (X∩Z) = 13% = 13/100
• (Y∩Z) = 10% = 10/100

We need to find (X∩Y∩Z)

We know that

(A∪B∪C) = (A) + (B) + (C) - (A∩B) - (A∩C) - (B∩C) + (A∩B∩C)

Assuming the people in the town speak at least one of the 3 languages,

(A∪B∪C) = 1

Hence,

(A) + (B) + (C) - (A∩B) - (A∩C) - (B∩C) + (A∩B∩C) = 1

or, (A∩B∩C) = 1 + (A∩B) + (A∩C) + (B∩C) - (A) - (B) - (C)

= 1 + 32/100 + 13/100 + 10/100 - 85/100 - 40/100 - 20/100

= (100 + 55 - 145)/100

= 10/100

= 10%

Hence, 10% of people speak all 3 languages.

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