in an office 3 4 of the can niether type nor..., Simplification, General Mathematics

Question:In an office ,`3/4` of the can niether type nor take shorthand .However `1/5th can type and `1/3` rd can take shorthand .What part of the whole staff can do both ?

A `1/5` 
B `3/40` 
C `13/40` 
D `17/60`

/94

+ AnswerD

+ ExplanationLet total number be x,

Then,the number who can type or take short hand 

`= (x - (3x)/4)`

`= x/4`.

Let A = set of person who can type & B = set of person who can take short hand .

`:. n (A∪B) =x/4,n(A)`

`= x/5 & n (B) = x/3`.

`Now n(A∩B) = n(A) + n (A∪B)`

`= (x/5 + x/3 - x/4)`

`= ((12x + 20x - 15x)/60)`

`= 17x/60`

`= 17/60`of the whole .

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