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

1. $20$%
2. $25$%
3. $40$%
4. $15$%
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Let the price of 100 cm of cloth be Rs 100. But he gets 120 cm of cloth for Rs 100.

Hence actual cost for 1 cm = 100/120 = Rs 5/6

Now instead  of selling 100 cm, by cheating, he sells 80 cm of cloth for the cost price of 100 cm of cloth.

To calculate profit, cost price of 80 cm of cloth = 80 * (5/6) = Rs 200/3

Selling price of 80 cm of cloth (actually 100 cm for the buyers)  at a discount of 20 % = 100*0.8 = Rs 80

Profit = $\frac{80- \frac{200}{3}}{\frac{200}{3}} = \frac{40}{200} = 20 \%$.

Option A is the Correct Answer.