price of an article is marked 40% above the cost price which is sold wirh 20% discount including 13% VAT at Rs. 6328.


i) Find the cost price os the article.
ii) find the Marked Price and VAT amount.
iii) What is the selling price without VAT? Also find the profit percentage for it.

Let's break down the problem step by step to find the required values.

### Given Data:
1. Marked price is 40% above the cost price.
2. A discount of 20% is given on the marked price.
3. VAT of 13% is included in the final selling price.
4. Final selling price, including VAT, is Rs. 6328.

### Objective:
1. Find the cost price of the article.
2. Find the marked price and VAT amount.
3. Find the selling price without VAT and the profit percentage.

---

### Step-by-Step Solution:

#### Step 1: Let the cost price be \( C \).

#### Step 2: Find the marked price.
The marked price is 40% above the cost price:
\[
\text{Marked Price} = C + 0.4C = 1.4C
\]

#### Step 3: Calculate the selling price after the discount.
The discount is 20% of the marked price:
\[
\text{Discounted Price} = \text{Marked Price} - \text{Discount} = 1.4C - 0.2 \times 1.4C = 1.4C \times (1 - 0.2) = 1.4C \times 0.8 = 1.12C
\]

#### Step 4: Calculate the selling price including VAT.
The final selling price after adding 13% VAT is given as Rs. 6328. This selling price includes VAT on the discounted price:
\[
\text{Selling Price with VAT} = \text{Discounted Price} + 13\% \text{ of Discounted Price} = 1.13 \times \text{Discounted Price}
\]
Substitute the given selling price:
\[
1.13 \times 1.12C = 6328
\]

#### Step 5: Solve for the cost price \( C \).
\[
1.2656C = 6328
\]
\[
C = \frac{6328}{1.2656} \approx 5000
\]

Thus, the cost price of the article is **Rs. 5000**.

---

### Calculate Other Values:

#### Step 6: Calculate the marked price.
\[
\text{Marked Price} = 1.4 \times 5000 = 7000
\]

#### Step 7: Calculate the VAT amount.
First, find the selling price without VAT:
\[
\text{Selling Price without VAT} = 1.12 \times 5000 = 5600
\]
Then, calculate the VAT amount:
\[
\text{VAT} = \text{Selling Price with VAT} - \text{Selling Price without VAT} = 6328 - 5600 = 728
\]

#### Step 8: Calculate the profit percentage.
\[
\text{Profit} = \text{Selling Price without VAT} - \text{Cost Price} = 5600 - 5000 = 600
\]
\[
\text{Profit Percentage} = \left(\frac{600}{5000}\right) \times 100 = 12\%
\]

---

### Final Answers:
1. **Cost Price:** Rs. 5000
2. **Marked Price:** Rs. 7000
3. **VAT Amount:** Rs. 728
4. **Selling Price without VAT:** Rs. 5600
5. **Profit Percentage:** 12%

Would you like to know more details or have any questions about the calculations?

---

### Related Questions:
1. What would be the selling price if no discount were applied?
2. How would the profit percentage change if VAT were 15% instead?
3. How does the selling price change with a 10% discount instead of 20%?
4. If the cost price increases by 10%, what will be the new marked price?
5. How to calculate profit percentage if the discount is given after adding VAT?
6. What is the effect of a higher VAT rate on the final selling price?
7. How would the final price be affected if the marked price was only 30% above the cost price?
8. What would happen to the profit percentage if there were no VAT applied?

### Tip:
To determine the final selling price accurately, always apply discounts before calculating VAT.

Learn how to calculate the cost price, marked price, selling price with VAT, and profit percentage using percentages and VAT calculations. This problem involves finding the cost price of an article marked 40% above the cost price, sold with a 20% discount and including 13% VAT at Rs. 6328. Suitable for Grades 9-12.

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