In a municipal office survey of 100 administrative officers, 50 officers speak English, 40… — State PSC Exam

In a municipal office survey of $100$ administrative officers, $50$ officers speak English, $40$ officers speak Hindi, and $20$ officers speak both English and Hindi. Based on this information, which of the following statements are correct?

The number of officers who speak only English is $30$ .Answer
The number of officers who speak neither English nor Hindi is $30$ .Answer
C
The number of officers who speak only Hindi is $40$ .
D
The total number of officers who speak at least one of the two languages is $90$ .

Answer

The correct statements are that the number of officers who speak only English is

30

, and the number of officers who speak neither English nor Hindi is

30

The number of officers speaking only English is obtained by subtracting the shared region (

20

) from the total English speakers (

50

), giving

30

. The officers speaking at least one language equals

30 \text{ (only English)} + 20 \text{ (both)} + 20 \text{ (only Hindi)} = 70

. Subtracting

70

from the total

100

officers gives

30

officers who speak neither language.

Step-by-Step Solution

Calculate the number of officers who speak only English.

\text{Only English} = 50 - 20 = 30

Subtract the intersection (both languages) from the total English speakers.

Calculate the number of officers who speak only Hindi.

\text{Only Hindi} = 40 - 20 = 20

Subtract the intersection (both languages) from the total Hindi speakers.

Calculate the total number of officers speaking at least one language (the union of sets).

\text{At least one language} = 30 + 20 + 20 = 70

Sum the exclusive counts and the shared intersection count.

Calculate the number of officers speaking neither language.

\text{Neither language} = 100 - 70 = 30

Subtract the number of officers speaking at least one language from the total group size.

Key Concept

Inclusion-Exclusion Principle for Two Sets

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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