The cost price of the two fans is the same. One fan is sold at a loss of 20% and the other fan is sold at a loss of 60%. What will be the overall loss percentage?

The cost price of the two fans is the same.

Let's assume the cost price of each fan is '100y'.

Sum of the cost price of both fans = 100y+100y = 200y    Eq.(i)

One fan is sold at a loss of 20%.

Selling price of the first fan = 100y of (100-20)%

= 100y of 80%

= 80y

the other fan is sold at a loss of 60%.

Selling price of second fan = 100y of (100-60)%

= 100y of 40%

= 40y

Sum of the selling price of both fans = 80y+40y = 120y    Eq.(ii)

Overall loss percentage = $$\frac{Eq.(i)-Eq.(ii)}{Eq.(i)}\times\ 100$$

= $$\frac{\left(200y-120y\right)}{200y}\times\ 100$$

= $$\frac{80y}{200y}\times\ 100$$

= 40%