Let the cost price of $1$ meter ($100$ cm) cloth be ₹ $100$.
So, the cost price of $120$ cm cloth is ₹ $100$.
The selling price of $80$ cm cloth $=80\%$ of ₹ $100=\dfrac{80}{100}\times100=$ ₹ $80$.
Cost price of $80$ cm cloth $= \dfrac{100}{120}\times80 = $₹ $\frac{200}{3}$
$\therefore$ Profit percentage $= \left(\dfrac{\text{SP – CP}}{\text{CP}}\right)\times100\%$
$\qquad \qquad \qquad \quad = \left(\dfrac{80-\frac{200}{3}}{\frac{200}{3}}\right)\times100\%$
$\qquad \qquad \qquad \quad = \left(\dfrac{\frac{240-200}{3}}{\frac{200}{3}}\right)\times100\%$
$\qquad \qquad \qquad \quad = \require{cancel} \dfrac{\cancel{40}^{20}}{\cancel{3}}\times\dfrac{\cancel{3}}{\cancel{2}\cancel{00}}\times1\cancel{00}\%$
$\qquad \qquad \qquad \quad=20\%.$
Correct Answer: $\text{A}$