in a certain office 72 of the workers prefer tea and..., Percentage, General Mathematics

Question:In a certain office, `72%` of the workers prefer tea and `445` coffee. If each of them prefers tea or coffee and `40` like both, the total number of workers in the office is :

A `200` 
B `240` 
C `250` 
D `320`

/114

+ AnswerC

+ ExplanationLet total number be x. Then,

`n(A) = 72/(100) x`

`= (18x)/55, n(B)`

`= (44)/(100) x`

`= (11x)/25 & n(AnnB)`

`= 40.`

`n (AuuB) = n(A) + n(B) - n(AnnB)`

`=> x = (18x)/25 + (11x)/25 - 40 => (29x)/25 - x`

`= 40 or (4x)/25`

`= 40`

`:. x = ((25 xx 40)/4)`

`= 250.`

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