There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi.10 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?
Step-by-step Solution:
Let's define the given data:
- Total students = 50
- Students who can speak both English and Hindi = 10
- Students who can speak English (including those who speak both) = 21
Now, let:
- \( x \) be the number of students who can speak Hindi.
- Students who can speak only English = Students who can speak English - Students who can speak both
\[
21 - 10 = 11
\]
- Students who can speak only Hindi = Students who can speak Hindi - Students who can speak both
\[
x - 10
\]
- The total number of students is the sum of students who can speak only English, only Hindi, and both languages:
\[
(21 - 10) + (x - 10) + 10 = 50
\]
\[
11 + x - 10 + 10 = 50
\]
\[
x + 11 = 50
\]
\[
x = 39
\]
Thus:
- Total students who can speak Hindi = 39
- Students who can speak only Hindi = 39 - 10 = 29
- Students who can speak only English = 11
The correct answer is:
D. 39, 29, and 11 respectively.