A shopkeeper marks an article at 60\% above its cost price. When he offers a discount of $4d\%$ on the marked price, he makes a profit of 28\%. If he instead offers a discount of $6d\%$, what will be the profit or loss percentage?

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**Solution:**

1. Let the cost price (CP) be Rs. 100x.

2. The marked price (MP) is 60\% above CP, so:
   $$	ext{MP} = 100x + 60\% 	imes 100x = 160x$$

3. When a discount of $4d\%$ is given, the shopkeeper earns 28\% profit. Therefore, the selling price (SP) is:
   $$	ext{SP} = 100x + 28\% 	imes 100x = 128x$$

4. Discount percentage on marked price is:
   $$\frac{	ext{MP} - 	ext{SP}}{	ext{MP}} 	imes 100 = \frac{160x - 128x}{160x} 	imes 100 = \frac{32x}{160x} 	imes 100 = 20\%$$

This means $4d = 20$, so $d = 5$.

5. Now, if the discount is $6d\% = 6 	imes 5 = 30\%$, the new selling price will be:
   $$	ext{New SP} = 	ext{MP} - 30\% 	imes 	ext{MP} = 160x - 0.30 	imes 160x = 112x$$

6. Calculate the profit or loss percentage with this new selling price:
   $$	ext{Profit/Loss \%} = \frac{	ext{SP} - 	ext{CP}}{	ext{CP}} 	imes 100 = \frac{112x - 100x}{100x} 	imes 100 = 12\% 	ext{ profit}$$

**Answer:** 12\% profit

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