If 20% of the goods are sold at 50% profit, 40% of the goods at 20% loss, 20% of the goods at 5% loss and the remaining at no loss or no profit, then the overall profit percentage is:

Let's assume the cost price of each good is Rs. 'y'.

Let's assume the total goods are '100z'.

The total cost price of all the goods = $$y \times 100z$$ = 100yz    Eq.(i)

If 20% of the goods are sold at 50% profit, 40% of the goods at 20% loss, 20% of the goods at 5% loss and the remaining at no loss or no profit.

The total selling price of all the goods = 20% of 100z of (100+50)% of y + 40% of 100z of (100-20)% of y + 20% of 100z of (100-5)% of y + 20% of 100z of y

= 20% of 100z of 150% of y + 40% of 100z of 80% of y + 20% of 100z of 95% of y + 20% of 100z of y

= 30yz + 32yz + 19yz + 20yz

= 101yz    Eq.(ii)

Overall profit percentage = $$\frac{\left(Eq.(ii)-Eq.(i)\right)}{Eq.(i)}\times100$$

= $$\frac{\left(101yz-100yz\right)}{100yz}\times100$$

= 1%