A number of friends decided to go on a picnic and planned to spend Rs.96 on eatables. Four of them, however did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was?

Options

A. 8
B. 16
C. 12
D. 24

Answer

A

Explanation

Let the number of persons who attended the picnic = x
Then, according to the question, `96/x - 96/(x + 4) = 4`
or `96/x = 4 + 96(x + 4) =(4(x + 4) + 96)/((x + 4))`
or `96/x = (4x + 16 + 96)/(x + 4)`
or, `96x + 384 = 4x^2 + 16x +96x `
or, `4x^2 + 16x - 384 = 0`
or, `4(x^2 + 4x - 96) = 0 `
or, `x^2 + 4x -96 = 0 `
or, `x^2 + 12x - 8x - 96 = 0 `
or, `(x + 12) (x-8)=0`
or, `x=-12 and x = 8`.
But, `x=-12 `is rejected.
[`because` No. of persons can.t be negative)
So, x = 8.
Therefore, the number of persons who attended the picnic = x=8.