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 ?

Answer: Option C

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