In a class of 50 students 25 take hindi and 16 take marathi.12 students take no languages. Find how many takes both hindi and marathi.
So only 38 students study either of the two languages
Number(H or M) = number(H) + number(M) - number(H and M)
38 = 25 + 16 - number(H and M)
number(H and M) = 3
or,
you can do it using a Venn diagram.
It may help to scale down the problem. In a class of 4 students, 2 take Hindi, 2 take Marathi, and 1 takes no languages.
Think of a pie having 50 slices.
The first 12 slices are the people taking neither language.
The next 25 slices are the people taking Hindi.
The next 16 slices are those taking Marathi.
( 12 + 25 + 16 ) slices = 53 slices
Three slice too many.
Thus the Hindi and Marathi pieces must overlap by 3 slices, which is the number of students taking both languages.
To find out how many students take both Hindi and Marathi, we need to use the concept of sets and the principle of inclusion-exclusion.
Given:
Total number of students = 50
Number of students taking Hindi = 25
Number of students taking Marathi = 16
Number of students taking neither Hindi nor Marathi = 12
Let's calculate the number of students taking both Hindi and Marathi using the principle of inclusion-exclusion:
Step 1: Calculate the number of students taking at least one of the languages (Hindi or Marathi):
Total number of students taking Hindi or Marathi = Number of students taking Hindi + Number of students taking Marathi
Let's calculate this:
Total number of students taking Hindi or Marathi = 25 + 16 = 41
Step 2: Subtract the number of students taking neither Hindi nor Marathi from the total number of students taking Hindi or Marathi:
Number of students taking both Hindi and Marathi = Total number of students taking Hindi or Marathi - Number of students taking neither Hindi nor Marathi
Let's calculate this:
Number of students taking both Hindi and Marathi = 41 - 12 = 29
Therefore, there are 29 students who take both Hindi and Marathi.