Let's reevaluate the calculations with the understanding that the correct answer is $x = 20$.

Step 1: Selling Price of Article A

Given $x = 20 \%$:

$\text{Selling Price of A} = 2800 \times \left(1 + \frac{20}{100}\right) = 2800 \times 1.2 = 3360$

Step 2: Selling Price of Article B

Markup of $2x \% = 40\%$:

$\text{Marked Price of B} = 8400 \times \left(1 + \frac{40}{100}\right) = 8400 \times 1.4 = 11760$

Discount of $x \% = 20\%$:

$\text{Selling Price of B} = 11760 \times \left(1 - \frac{20}{100}\right) = 11760 \times 0.8 = 9408$

Step 3: Calculate Total Selling Price (TSP)

$\text{TSP} = 3360 + 9408 = 12768$

Step 4: Calculate the Overall Profit Percentage

Total Cost Price (TCP): $\text{TCP} = 2800 + 8400 = 11200$

Overall profit: $\text{Overall Profit} = 12768 - 11200 = 1568$

Overall profit percentage: $\text{Overall Profit Percentage} = \frac{1568}{11200} \times 100 \approx 14\%$

Step 5: Relate to Given Information

We were given that the overall profit percentage is $x - 6$ where $x = 20$:

$x - 6 = 14\%$

This calculation confirms that when $x = 20$, the overall profit percentage matches the given condition, confirming that $x = 20$ is indeed correct.

Would you like any more clarification or details on this solution?

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Relative Questions:

1. What is the formula for calculating profit percentage in different scenarios?
2. How would the profit change if the cost price of Article B were higher?
3. How does changing the discount percentage affect the overall profit?
4. Can this method be used to calculate losses as well?
5. What happens to the profit percentage if the markup is equal to the discount?
6. How can one verify such calculations using algebraic methods?
7. What strategies can be employed to maximize profit when selling multiple items?
8. How would adding another type of article affect the overall profit percentage?

Tip: Remember to always check the final result against the given conditions in a problem to ensure consistency.