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Instead of a metre scale, a cloth merchant uses a $120\; \text{cm}$ scale while buying, but uses an $80\; \text{cm}$ scale while selling the same cloth. If he offers a discount of $20 \%$ on cash payment, what is his overall profit percentage?

1. $20\%$
2. $25\%$
3. $40\%$
4. $15\%$

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 ₹ $100=\frac{80}{100}\times100= ₹ 80$.

Cost price of $80$ cm cloth $= \frac{100}{120}\times80 = ₹ \frac{200}{3}$

$\therefore$ Profit percentage $= \left(\frac{\text{SP – CP}}{\text{CP}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \left(\frac{80-\frac{200}{3}}{\frac{200}{3}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \left(\frac{\frac{240-200}{3}}{\frac{200}{3}}\right)\times100\%$

$\qquad \qquad \qquad \quad = \require{cancel} \frac{\cancel{40}^{20}}{\cancel{3}}\times\frac{\cancel{3}}{\cancel{2}\cancel{00}}\times1\cancel{00}\%$

$\qquad \qquad \qquad \quad=20\%.$

Correct Answer: $\text{A}$
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