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.
3 answers
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.
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.
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.
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.