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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:------------------

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## Answers

### This Is a Certified Answer

**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**