A small confectioner bought a certain number of pastries flavoured pineapple, mango and black-forest from the bakery, giving for each pastry as many rupees as there were pastry of that kind;altogether he bought 23 pastries and spent Rs.211; find the number of each kind of pastry that he bought, if mango pastry are cheaper than pineapple pastry and dearer than black-forest pastry.

Given that cost of a type of pastry is equal to the quantity bought

if x,y,z are the no. of pastries bought of each type then $$x^2+y^2+z^2$$ = 211 and x+y+z = 23

Using options,

option A = 10,9,4 i.e. 100+81+16 = 197 therefore cannot be the answer

option B= 11, 9, 3 i.e. 121+81+9 = 211 Therefore is our answer

option C = 10, 8 , 5 i.e. 100+64+25 = 189 therefore cannot be the answer

option D = 11, 8, 4 i.e. 121+64+16 = 201 therefore cannot be the answer

Therefore our answer is option 'B'