Question

A fruit seller sells half of his fruits plus half an orange ,again he sells half of what remains plus half an orange , and so again a third time . His store is now exhausted , how many did he start from

a) 5     b)  7   c) 9  4)11

Answer 1

Let he has x fruits in the beginning..
He sells half of his stock and 1/2 oranges. 
number of fruits sold by him in the first instance = (x/2)+1/2
remaining fruits = x-[(x/2)+1/2]= (x/2)-1/2

number of fruits sold by him in the second instance = (1/2) [(x/2)-1/2]+1/2 = (x+1)/4
remaining fruits after the second sale = (x-1)/2 - (x+1)/4= (x-3)/4

now,number of fruits sold by him in the third instance =(1/2)[(x-3)/4]+1/2 = (x+1)/8
remaining fruits after the third sale = (x-3)/4 - (x+1)/8=(x-7)/8
now, his store is exhausted after the third sale
so ,(x-7)/8 = 0=>x=7
so he started with 7 fruits initially..

Comments

Thank you very much GATE

Answer 2

7 he will start