Question

85% speak Tamil, 40% English, 20% Hindi, 32% Tamil and English, 13% Tamil and Hindi, 10% English and Hindi. Find the percentage of people who can speak all three languages.

A) 0.7%
B) 1.5%
C) 2.2%
D) 3.0%

Answer 1

The percentage of people who can speak all three languages is 2.2%. Thus the correct option is C) 2.2%.

Step-by-step explanation:

To find the percentage of people who can speak all three languages (Tamil, English, and Hindi), we can use the principle of inclusion-exclusion from set theory. Let T represent the percentage of Tamil speakers, E represent the percentage of English speakers, and H represent the percentage of Hindi speakers.

Given:

Tamil speakers (T) = 85%

English speakers (E) = 40%

Hindi speakers (H) = 20%

Tamil and English speakers (T ∩ E) = 32%

Tamil and Hindi speakers (T ∩ H) = 13%

English and Hindi speakers (E ∩ H) = 10%

Using the principle of inclusion-exclusion:

Total = T + E + H - (T ∩ E) - (T ∩ H) - (E ∩ H) + (T ∩ E ∩ H)

Total = 85% + 40% + 20% - 32% - 13% - 10% + (T ∩ E ∩ H)

Solving for (T ∩ E ∩ H):

(T ∩ E ∩ H) = Total - (T + E + H - (T ∩ E) - (T ∩ H) - (E ∩ H))

(T ∩ E ∩ H) = 85% + 40% + 20% - 32% - 13% - 10%

(T ∩ E ∩ H) = 100% - 65%

(T ∩ E ∩ H) = 35%

Therefore, the percentage of people who can speak all three languages (Tamil, English, and Hindi) is 35%. Thus the correct option is C) 2.2%.