a number of friends decided to go on a picnic and planed..., Simplification, General Mathematics

Question:A number of friends decided to go on a picnic and planed to spend Rs `96` on eatables. Four of them ,did not turn up.As a consequence, the remaining ones had to contributed Rs `4` each extra.The number of these who attended the picic was

A `24` 
B `16` 
C `12` 
D `8`

/94

+ AnswerD

+ ExplanationSuppose total number = x.Then,

`96/(x - 4) - 96/x = 4`

`or 1/(x - 4) - 1/x = 4/96`

`or x- (x - 4)/x(x - 4) = 1/24`

`or x^2 - 4x - 96 = 0`

`or (x - 12)(x + 8) = 0`

`or x = 12`.

:. Number of students attending the picnic 

`= (12 - 4) = 8`

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