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

Correct Option (D)

Let E denote the set of students who can speak English, and H denote the set of students who can speak Hindi.

• Total number of students = 50.
• Number of students who can speak both English and Hindi = 10.
• Number of students who can speak English = 21.

First, calculate the number of students who can speak only English:

• Students speaking only English = (Total students speaking English) - (Students speaking both English and Hindi)
• Students speaking only English = 21 - 10 = 11.

Next, calculate the number of students who can speak only Hindi:

• Total students = (Students speaking only English) + (Students speaking only Hindi) + (Students speaking both English and Hindi)
• 50 = 11 + (Students speaking only Hindi) + 10
• 50 = 21 + (Students speaking only Hindi)
• Students speaking only Hindi = 50 - 21 = 29.

Finally, calculate the total number of students who can speak Hindi:

• Total students speaking Hindi = (Students speaking only Hindi) + (Students speaking both English and Hindi)
• Total students speaking Hindi = 29 + 10 = 39.

Therefore, the number of students who can speak Hindi, only Hindi, and only English are 39, 29, and 11, respectively.

Incorrect Options:

Options (A), (B), and (C) are incorrect as their respective values for the number of students who can speak Hindi, only Hindi, and only English do not align with the calculations derived from the given data.