Sure, let's go through each part of the question step-by-step:
2) The marked price of a watch is Rs.5000 at a shop
a) What is VAT? Define it
VAT, or Value-Added Tax, is a type of indirect tax that is levied on the consumption of goods and services. It is added to the selling price of a product and is paid by the end consumer. The amount of VAT a consumer pays is based on the value of the product at each stage of its production or distribution.
b) What will be the price of the watch if 13% VAT is added without allowing any discount?
- The marked price of the watch is Rs.5000.
- The VAT rate is 13%.
To find the price of the watch with VAT:
- Calculate the VAT amount: [tex]\( \text{VAT amount} = \text{Marked Price} \times \text{VAT Rate} \)[/tex]
- [tex]\( \text{VAT amount} = 5000 \times 0.13 = 650 \)[/tex]
- Add the VAT amount to the marked price to get the final price:
- [tex]\( \text{Final Price} = \text{Marked Price} + \text{VAT amount} \)[/tex]
- [tex]\( \text{Final Price} = 5000 + 650 = 5650 \)[/tex]
Therefore, the price of the watch after adding 13% VAT without any discount is Rs.5650.
c) By what percent will the VAT amount on the watch be reduced when a 15% discount is given, in comparison to no discount at all?
- The marked price is Rs.5000.
- The discount rate is 15%.
- The VAT rate remains at 13%.
To find the price after applying the discount:
- Calculate the discounted price: [tex]\( \text{Discounted Price} = \text{Marked Price} \times (1 - \text{Discount Rate}) \)[/tex]
- [tex]\( \text{Discounted Price} = 5000 \times (1 - 0.15) = 5000 \times 0.85 = 4250 \)[/tex]
To calculate the VAT on the discounted price:
- [tex]\( \text{VAT with Discount} = \text{Discounted Price} \times \text{VAT Rate} \)[/tex]
- [tex]\( \text{VAT with Discount} = 4250 \times 0.13 = 552.5 \)[/tex]
To find the original VAT amount (without discount):
- [tex]\( \text{VAT without Discount} = 5000 \times 0.13 = 650 \)[/tex]
The reduction in the VAT amount is:
- [tex]\( \text{VAT Reduction} = \text{VAT without Discount} - \text{VAT with Discount} \)[/tex]
- [tex]\( \text{VAT Reduction} = 650 - 552.5 = 97.5 \)[/tex]
The percentage reduction in the VAT amount is calculated as:
- [tex]\( \text{VAT Reduction Percent} = \left( \frac{\text{VAT Reduction}}{\text{VAT without Discount}} \right) \times 100 \)[/tex]
- [tex]\( \text{VAT Reduction Percent} = \left( \frac{97.5}{650} \right) \times 100 \approx 15\% \)[/tex]
Therefore, the VAT amount on the watch is reduced by 15% when a 15% discount is applied, compared to no discount at all.
