IIFT 2016 Question Paper Question 107

Question 107

A playschool contains 4 boys and y girls. On every Wednesday during winter, five students, of which at least three are boys, go to Zoological Garden, a different group being sent every week. At the Zoological Garden, each boy in the group is given a ball. If the total number of balls distributed is 368, then the value of y is


Total 5 students out of 4 boys and y girls can be chosen in two ways :

(1)  3 Boys and 2 Girls = $$4c_{3}*$$y$$c_{2}$$

(2)  4 Boys and 1 Girls = $$4c_{4}*$$y$$c_{1}$$

So total number of balls given to boys :

                       3*$$4c_{3}*$$y$$c_{2}$$+4*$$4c_{4}*$$y$$c_{1}$$ = 368

                            $$6(y)(y-1)+4y$$ = 368

                            6$$y^{2}-2y-368$$ = 0

                            3$$y^{2}-y-184$$ = 0

                            $$(y-8)(3y+23)$$ = 0

                            $$y=8$$,  y $$\neq$$ $$ \frac{-23}{3}$$

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