# Difficult Puzzle! In a class consisting of 100 students 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi...In a class consisting of 100 students 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. How many students know both Hindi and English?

1
by chuVpooravy

2015-10-18T14:09:48+05:30

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Draw a venn diagram for clearly understanding the numbers and sets.

See diagram and then understand the solution.

let A = set  of students knowing English only.
B = set of those knowing English and Hindi.
C = set of those knowing only Hindi
D = set of those who know neither.

A+B+C+D = 100    total.    given
A+B = 20    English.  given

those not knowing Hindi = 20  given
B+C =  those knowing Hindi  = 100  - 20  = 80
D = 10  given

A+B+ B+C + D = 20 + 80  + 10 = 110
=>  A + 2 B + C + D = 110
So  B = 10    this is the answer

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