The cost price of an article is Rs 500. A shopkeeper marks the price of the article at $X\%$ above the cost price. If he offers a discount of 20\% on the marked price and still makes a profit of 4\%, find the value of $X$.

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**Solution:**

1. Let the cost price (CP) be Rs 500.

2. The marked price (MP) is $X\%$ above the cost price, so:
   $$ MP = 500 + \frac{X}{100} 	imes 500 = 500 	imes \left(1 + \frac{X}{100}ight) $$

3. The shopkeeper gives a 20\% discount on the marked price, so the selling price (SP) is:
   $$ SP = MP 	imes (1 - 0.20) = MP 	imes 0.80 $$

4. The shopkeeper earns a profit of 4\%, so:
   $$ SP = CP 	imes (1 + 0.04) = 500 	imes 1.04 = 520 $$

5. Substitute $SP = 0.80 	imes MP$ and $MP = 500 	imes \left(1 + \frac{X}{100}ight)$:
   $$ 0.80 	imes 500 	imes \left(1 + \frac{X}{100}ight) = 520 $$

6. Simplify:
   $$ 400 	imes \left(1 + \frac{X}{100}ight) = 520 $$

7. Divide both sides by 400:
   $$ 1 + \frac{X}{100} = \frac{520}{400} = 1.3 $$

8. Subtract 1 from both sides:
   $$ \frac{X}{100} = 0.3 $$

9. Multiply both sides by 100:
   $$ X = 30 $$

**Answer:** $30$

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