A shopkeeper advertises for selling cloth at 4% loss. However, by using a false meter scale he actually gains 20% . What is the actual length of the scale ?

Let the percentage deduction in weight be y%
Then,
$$\eqalign{ & \frac{{y - 4}}{{100 - y}} \times 100 = 20 \cr & \Rightarrow \frac{{y - 4}}{{100 - y}} = \frac{1}{5} \cr & \Rightarrow 5y - 20 = 100 - y \cr & \Rightarrow 6y = 120 \cr & \Rightarrow y = 20 \cr} $$
Hence, for a meter, length used = (100 - 20)% of 1 m
= 80% of 100 cm = 80 cm