a bicycle is sold at Rs.9605 with 15% discount including VAT of 13%.

Find the MP.
Find the d amt.


To find the Marked Price (MP) and the discount amount (d amt) of the bicycle, we will work through the given details step by step.

### Given Data:
- Selling Price (SP) after discount and including VAT: Rs. 9605
- Discount: 15%
- VAT: 13%

### Steps to Solve:

1. **Determine the Selling Price before VAT:**
   The Selling Price after VAT is given, so we need to remove the VAT component to find the original Selling Price before VAT.

   Let's denote the Selling Price before VAT as \( SP_{before} \).

   VAT is added to the price, so:
   \[
   SP_{after} = SP_{before} + (13\% \times SP_{before})
   \]

   Given:
   \[
   SP_{after} = 9605
   \]

   Therefore:
   \[
   9605 = SP_{before} \times (1 + 0.13) = SP_{before} \times 1.13
   \]

   Solving for \( SP_{before} \):
   \[
   SP_{before} = \frac{9605}{1.13} = 8500
   \]

2. **Determine the Marked Price (MP):**
   The Selling Price before VAT (Rs. 8500) includes the discount. We need to find the original Marked Price before the discount was applied.

   Let's denote the Marked Price as \( MP \).

   Given a discount of 15%, the Selling Price before VAT is:
   \[
   SP_{before} = MP - (15\% \times MP)
   \]

   Therefore:
   \[
   8500 = MP \times (1 - 0.15) = MP \times 0.85
   \]

   Solving for \( MP \):
   \[
   MP = \frac{8500}{0.85} = 10000
   \]

3. **Determine the Discount Amount:**
   The discount amount is the difference between the Marked Price and the Selling Price before VAT.

   \[
   \text{Discount Amount} = MP - SP_{before} = 10000 - 8500 = 1500
   \]

### Summary:
- **Marked Price (MP):** Rs. 10000
- **Discount Amount (d amt):** Rs. 1500

Would you like any further details or have any questions?

Here are some related questions for further exploration:

1. How would the calculations change if the VAT rate was different?
2. What would be the new SP after VAT if the discount was 20% instead of 15%?
3. How to find the Selling Price if the Marked Price and the discount percentage are known, but without VAT?
4. How to calculate the percentage discount given the Marked Price and the final Selling Price after VAT?
5. How does a change in VAT affect the final Selling Price?
6. What if there were additional charges along with VAT, how would that affect the calculations?
7. How to compute the final price if a discount is applied after adding VAT instead of before?
8. How does the inclusion of VAT impact the perception of discounts?

**Tip:** When dealing with percentage-based problems, always break down the problem into clear steps, focusing on one percentage adjustment at a time.

Learn how to calculate the Marked Price (MP) and Discount Amount (d amt) of a product sold with VAT and a discount. This problem covers percentage calculations and VAT inclusion in pricing. Suitable for students in Grades 9-12.

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