Let's break down the problem step by step:

Step 1: Define Variables

• Cost price (C.P.) = Rs 5000
• Marked price = Rs $5000 \times (1 + \frac{x}{100})$, where $x$ is the percentage increase over the cost price.
• First discount = Rs 1000
• Second discount = 20%

After applying the discounts, the article is sold for a price that gives a profit of Rs 1000. So, the selling price (S.P.) is: $S.P. = C.P. + 1000 = 5000 + 1000 = 6000$

Step 2: Apply the Discounts

1. After the first discount of Rs 1000, the price is reduced to: $\text{Price after first discount} = \text{Marked price} - 1000$

2. After the second discount of 20%, the price becomes: $\text{Final selling price} = \text{Price after first discount} \times (1 - 0.20) = 0.80 \times (\text{Marked price} - 1000)$

Since the final selling price is Rs 6000, we can set up the following equation: $0.80 \times (\text{Marked price} - 1000) = 6000$

Step 3: Solve for the Marked Price

1. First, simplify the equation: $0.80 \times (\text{Marked price} - 1000) = 6000$ $\text{Marked price} - 1000 = \frac{6000}{0.80}$ $\text{Marked price} - 1000 = 7500$ $\text{Marked price} = 7500 + 1000 = 8500$

Step 4: Find the Value of $x$

The marked price is also given by: $\text{Marked price} = 5000 \times \left(1 + \frac{x}{100}\right)$ We already know that the marked price is Rs 8500, so: $8500 = 5000 \times \left(1 + \frac{x}{100}\right)$ Now, solve for $x$: $1 + \frac{x}{100} = \frac{8500}{5000}$ $1 + \frac{x}{100} = 1.7$ $\frac{x}{100} = 0.7$ $x = 70$

Final Answer:

The value of $x$ is 70%.

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Would you like a more detailed explanation or have any further questions? Here are 5 related questions for further practice:

1. How do successive discounts affect the final price compared to a single discount?
2. How would the profit change if the first discount was larger than the second?
3. If the cost price was Rs 6000, what would the value of $x$ be in this case?
4. How do you calculate the profit percentage in such scenarios?
5. What happens to the selling price if the second discount is increased to 30%?

Tip: Always apply the successive discounts step by step, and remember that each discount is applied on the reduced price after the previous discount.