Total number of products sold by shop A in all three days is 246 more than the combined total number of products sold by shops C and E on Monday. Given that the total number of products sold by A on Monday and Wednesday are equal, find the ratio of *x* to *y*.

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**Solution:**

1. For shop E, the total products sold on Monday and Tuesday together is 70% of total sales.
   - Given: 70% of total sales = 15x
   - Therefore, 100% of total sales = $ \frac{15x}{70} \times 100 = \frac{75x}{2} $

2. For shop C, total products sold on Monday and Tuesday is 80% of total sales.
   - Given: 80% of total sales = 10x
   - So, 100% of total sales = $ \frac{10x}{80} \times 100 = 12.5x $

3. Given the difference between total products sold by shops C and E in all three days is 120:
   - $ \frac{75x}{2} - 12.5x = 120 $
   - Simplifying: $ 37.5x - 12.5x = 120 $
   - $ 25x = 120 $
   - $ x = 4.8 $

4. Total products sold by shop D in all three days is 120.

5. Total products sold by shop A in all three days is 246 more than the combined products sold by shops C and E on Monday:
   - Total products sold by C and E on Monday = $ \frac{4}{9} \times 10x + \frac{3}{7} \times 15x $ (ratios from given data)
   - Calculate these values using $ x = 4.8 $

6. Given total products sold by A on Monday and Wednesday are equal, let each be $ a $.
   - Total products sold by A in three days = $ 2a + \text{Tuesday sales} = 400 $ (from data)
   - $ 2a = 300 $ so $ a = 150 $

7. Calculate $ y $ as percentage of products sold on Wednesday out of total sales by A:
   - $ y = \frac{450x}{100} = 75 $

8. Finally, the required ratio $ \frac{x}{y} = \frac{8}{7} = 16:75 $.

**Answer:** 16:75

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