A fruit-seller sells half of his fruits plus 4 oranges; again he sells half of what remains plus 4 o

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09 Aug 2013 Fruit-seller

A fruit-seller sells half of his fruits plus 4 oranges; again he sells half of what remains plus 4 oranges; and so again a third time. His store is now exhausted; How many did he start with?

OPtion

1) 14
2) 24
3) 28
4) 32
5) 36
6) 42
7) 56
8) 60
9) 64
10)None of these

Solution

Let he has x fruits in the beginning.
He sells half of his stock and 4 oranges.
Number of fruits sold by him in the first instance = (x/2)+4
The remaining fruits = x-[(x/2)+4]= (x/2)-4
Number of fruits sold by him in the second instance =
=(1/2)[(x/2)-4]+4 = (x/4)-2+4 = (x/4)+2
Balance of fruits after the second sale = [(x/2)-4]-[(x/4)+2]
= (x/4)-6
Similarly Number of fruits sold by him in the third instance
= (1/2)[(x/4)-6]+4 = (x/8)-3+4 = (x/8)+1
Balance of fruits after the third sale = [(x/4)-6]-[(x/8)+1]=(x/8)-7
According to the question, his store is exhausted after the third sale
so (x/8)-7 = 0
x = 56 ..... To start with, there were 56 fruits
option 7
total fruit structure after the sale
total other fruit orange
initial 56 44 12
after first sale (28+4) 24 16 8
after second sale(12+4) 8 4 4
after third sale (4+4) 0 0 0

Correct Option: 7 Best Solution (0)