Let the total number of fruits= 5x.
Therefore, the number of mangoes in the stock= (40/100)*5x= 2x.
Let the number of apples= 5y.
He sold x mangoes, 96 bananas and 2y apples which is equal to 50% of the total fruits.
x+ 96+ 2y= 2.5x
2x+192+4y= 5x
192+ 4y= 3x
The smallest value of y which will satisfy the equation is y= 3.
192+ 12= 204= 3x
x= 68
The smallest possible total number of fruits in the stock at the beginning of the day is 5x= 5*68= 340.

The question is "A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is"

Hence, the answer is '340'