Question

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, only Hindi and only English?

Answer 1

Hint: Number of students who speaks Hindi will be equal to Total number of students minus number of students who speaks only English, Number of students who speaks only Hindi will be equal to Number of Hindi speaking students minus number of students who speaks both English and Hindi and Number of students who speaks only English will be equal to Number of students who speak only English minus number of students who speaks both English and Hindi.

Complete step by step solution:
Given,
Total number of students \[ = 50\]
Number of students who can speak both English and Hindi \[ = 10\]
Number of students who can speak English \[ = 21\]
Number of students who speaks Hindi \[ = \] Total number of students \[ - \] Number of students who speaks only English
\[ = 50 - 11\]
\[ = 39\]
Number of students who speaks only Hindi\[ = \] Number of students who speaks Hindi \[ - \] Number of students who can speak both English and Hindi
\[ = 39 - 10\]
\[ = 29\]
Number of students who speaks only English\[ = \] Number of students who can speak English\[ - \] Number of students who can speak both English and Hindi
\[ = 21 - 10\]
\[ = 11\]
Therefore, \[39\] students can speak Hindi, \[29\] students can speak only Hindi and \[11\] students can speak only English.

Note: We have to keep in mind that in the question it is given that the number of students who can speak English is \[21\], one might get confused that it is the students who speak only English but it contains both types of students, one who speaks only English and other who can speak English and Hindi both.