Math riddle?

There are 100 students ( 75 speak English, 83 of them speak German, 10 of them dont speak any language) How many of this students speak two languages.

There are 100 students ( 75 speak English, 83 of them speak German, 10 of them don't speak any language) How many of this students speak two languages.

or:There are 100 students ( 75 speak English, 83 of them speak German, 10 of them don't speak any language) How many of this students speak two languages.

or:75 people speak 2 languages

or:10 students don't speak any language. From 100 students this leaves 90.83 - (90 - 75) = 68or if we start with the English speakers75 - (90 - 83) = 6868 students speak two languages.You have to identify the intersection (or the overlap) between the two sets of students. 0.......7............................................75................90..........100|--------- eng = 75 ------------------------|..........|------------- ger = 83 -----------------------------|..........|---------- overlap = 68 ----------|The overlap of [7,75[ = 75 - 7 = 68 is the solution. My little diagram serves just to help visualise the idea but with the quite limited means of this editor it's obviously not true to scale.

or:Let The Number Of students who speak English be n(A)Let The Number Of students who speak German be n(B)Therefore, n(A) = 75 and n(B) = 83Total Number of Students are :- n(A union B) = 110But ten students speak neither English Nor GermanSo, total no. of students = 110 - 10 = 100By Identity, n(A union B) = n(A) + n(B) - n(A intersection B)Therefore, 100 = 75 + 83 - n(A intersection B)Therefore, - n(A intersection B) = 100 - 158Therefore, - n(A intersection B) = - 58Therefore, n(A intersection B) = 58So, The Number Of Students who Speak Both The Languages are 58

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