A number of friends decided to go on a picnic and planned to spend rs.108 on eatables. three of them however did not turn up. as a consequence each one of the remaining had to contribute rs. 3 extra. the number of them who attended the picnic was:------------------ explain please

1
by iitjeepraveen

2015-01-24T13:37:57+05:30

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Let n be the original number of friends

& r = Rs per student

then, nr = 108 ⇒r = 108/n

As 3 friends did not turn up so each friend has to pay Rs 3 extra then;

(n-3) (r+3) = 108

nr + 3n -3r - 9 = 108

n(108/n) + 3n - 3(108/n) -9 = 108

108 + 3n - 3*108/n - 9 = 108

3n - 3*108/n - 9 = 0

3n^2 - 3*108 - 9n = 0

Taking 3 common, we get n^2 - 3n - 108 = 0

Roots of the above quadratic equation =  (3 + √9+432)/2 ; (3-√9+432)/2

(3+√441)/2  ;  (3 - √441)/2

(3+21)/2  ; (3 -21)/2

24/2 ; -18/2

Neglecting the negative value, we have x = 12 Hence the number of friends who attended the picnic = (x-3) = 12-3 = 9