Question

There are 50 students in a class. Some can speak only English and some can speak only Hindi. Ten students can speak both Hindi and English. If the number of students who can speak English is 21, then how many students can speak only Hindi, and how many students can speak only English ?

• A. 39, 29 and 11 respectively
• B. 37, 27 and 13 respectively
• C. 28, 18 and 22 respectively
• D. 27, 11 and 29 respectively

Hint:

Use set theory and the principle of inclusion-exclusion to solve language-based problems.

Answer 1

The Correct Option is A

Total students = 50 Students speaking both Hindi and English = 10 Students speaking English = 21 Number of students speaking only English = Total English speakers - Both Only English = \( 21 - 10 = 11 \) Number of students speaking only Hindi = Total students - (Only English + Both) Only Hindi = \( 50 - (11 + 10) = 50 - 21 = 29 \) The question asks for (Only Hindi, Only English), which is (29, 11). Option (1) gives "39, 29 and 11 respectively". If the format is (Total Hindi Speakers, Only Hindi, Only English), then: Total Hindi Speakers = Only Hindi + Both = \( 29 + 10 = 39 \) This matches option (1). So, the interpretation of what the options represent is crucial here. Assuming the options are in the format (Total Hindi Speakers, Only Hindi Speakers, Only English Speakers): Total Hindi Speakers = 39 Only Hindi Speakers = 29 Only English Speakers = 11 This aligns with option (1).