The ratio of the cost price to the selling price of an article is $4:7$, and the ratio of the marked price to the selling price is $36:35$. If the markup on the article is Rs $160$, what is the profit earned on the article (in Rs)?

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**Solution:**

1. Let the selling price be $7x$ and the cost price be $4x$ (from the ratio $4:7$).

2. The ratio of marked price to selling price is $36:35$, so marked price = $\frac{36}{35} 	imes 7x = \frac{36}{35} 	imes 7x = \frac{252}{35}x = \frac{36}{5}x$.

3. Markup price is the difference between marked price and cost price:
   $$	ext{Markup} = 	ext{Marked Price} - 	ext{Cost Price} = \frac{36}{5}x - 4x = \left(\frac{36}{5} - 4ight)x = \left(\frac{36 - 20}{5}ight)x = \frac{16}{5}x$$

4. Given markup price is Rs $160$, so:
   $$\frac{16}{5}x = 160 \implies x = \frac{160 	imes 5}{16} = 50$$

5. Profit is the difference between selling price and cost price:
   $$	ext{Profit} = 7x - 4x = 3x = 3 	imes 50 = 150$$

**Answer:** Rs $150$

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