Answer :
Sure, let's proceed with solving these questions step by step.
### Part 1: Finding the Marked Price of the Camera
Given:
- Payment after discount and VAT: Rs. 15,175.90
- Discount rate: 15%
- VAT rate: 13%
To find the marked price (let's denote it as [tex]\( P \)[/tex]), we need to work backwards from the final payment.
1. Let’s denote the marked price as [tex]\( P \)[/tex].
2. First, calculate the discounted price. A 15% discount on the marked price means the customer pays 85% of [tex]\( P \)[/tex]:
[tex]\[ \text{Discounted Price} = P \times (1 - 0.15) = 0.85P \][/tex]
3. Then, VAT is added to the discounted price. Hence, the price after VAT is applied:
[tex]\[ \text{Payment After VAT} = \text{Discounted Price} \times (1 + 0.13) = 0.85P \times 1.13 = 0.9605P \][/tex]
4. We know that:
[tex]\[ 0.9605P = 15175.90 \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{15175.90}{0.9605} \approx 15800 \][/tex]
So, the marked price of the camera is approximately Rs. 15,800.
### Part 2: Khukuri Purchase
Given:
- VAT refund: Rs. 1,170
- Discount rate: 25%
- VAT rate: 13%
To answer the questions related to the Khukuri purchase:
(a) What does the Rs. 1,170 represent?
Rs. 1,170 represents the VAT amount, which is refunded to the tourist. It means the VAT calculated on the discounted price is Rs. 1,170.
(b) What was the label price?
1. Let’s denote the discounted price as [tex]\( D \)[/tex].
2. Since the VAT refund is Rs. 1,170 and the VAT rate is 13%, [tex]\( D \)[/tex] can be found as:
[tex]\[ \text{VAT Amount} = D \times 0.13 \][/tex]
[tex]\[ 1170 = D \times 0.13 \][/tex]
Solving for [tex]\( D \)[/tex]:
[tex]\[ D = \frac{1170}{0.13} \approx 9000 \][/tex]
3. The label price can be found by reversing the discount calculation:
[tex]\[ D = P \times (1 - \text{Discount Rate}) = P \times (1 - 0.25) = 0.75P \][/tex]
[tex]\[ 9000 = 0.75P \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{9000}{0.75} = 12000 \][/tex]
So, the label price of the Khukuri is Rs. 12,000.
(c) Find the discounted amount.
The discounted amount is the difference between the label price and the discounted price:
[tex]\[ \text{Discounted Amount} = P - D = 12000 - 9000 = 3000 \][/tex]
The discounted amount is Rs. 3,000.
(d) What was the amount that is paid by the tourist at the shop? Calculate it.
The amount paid by the tourist includes the discounted price plus the VAT:
[tex]\[ \text{Amount Paid} = D + \text{VAT} = 9000 + 1170 = 10170 \][/tex]
The amount paid by the tourist at the shop is Rs. 10,170.
### Summary:
- The marked price of the camera: Rs. 15,800
- Rs. 1,170 represents the VAT amount refunded to the tourist.
- The label price of the Khukuri: Rs. 12,000
- The discounted amount: Rs. 3,000
- The amount paid by the tourist at the shop: Rs. 10,170
### Part 1: Finding the Marked Price of the Camera
Given:
- Payment after discount and VAT: Rs. 15,175.90
- Discount rate: 15%
- VAT rate: 13%
To find the marked price (let's denote it as [tex]\( P \)[/tex]), we need to work backwards from the final payment.
1. Let’s denote the marked price as [tex]\( P \)[/tex].
2. First, calculate the discounted price. A 15% discount on the marked price means the customer pays 85% of [tex]\( P \)[/tex]:
[tex]\[ \text{Discounted Price} = P \times (1 - 0.15) = 0.85P \][/tex]
3. Then, VAT is added to the discounted price. Hence, the price after VAT is applied:
[tex]\[ \text{Payment After VAT} = \text{Discounted Price} \times (1 + 0.13) = 0.85P \times 1.13 = 0.9605P \][/tex]
4. We know that:
[tex]\[ 0.9605P = 15175.90 \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{15175.90}{0.9605} \approx 15800 \][/tex]
So, the marked price of the camera is approximately Rs. 15,800.
### Part 2: Khukuri Purchase
Given:
- VAT refund: Rs. 1,170
- Discount rate: 25%
- VAT rate: 13%
To answer the questions related to the Khukuri purchase:
(a) What does the Rs. 1,170 represent?
Rs. 1,170 represents the VAT amount, which is refunded to the tourist. It means the VAT calculated on the discounted price is Rs. 1,170.
(b) What was the label price?
1. Let’s denote the discounted price as [tex]\( D \)[/tex].
2. Since the VAT refund is Rs. 1,170 and the VAT rate is 13%, [tex]\( D \)[/tex] can be found as:
[tex]\[ \text{VAT Amount} = D \times 0.13 \][/tex]
[tex]\[ 1170 = D \times 0.13 \][/tex]
Solving for [tex]\( D \)[/tex]:
[tex]\[ D = \frac{1170}{0.13} \approx 9000 \][/tex]
3. The label price can be found by reversing the discount calculation:
[tex]\[ D = P \times (1 - \text{Discount Rate}) = P \times (1 - 0.25) = 0.75P \][/tex]
[tex]\[ 9000 = 0.75P \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{9000}{0.75} = 12000 \][/tex]
So, the label price of the Khukuri is Rs. 12,000.
(c) Find the discounted amount.
The discounted amount is the difference between the label price and the discounted price:
[tex]\[ \text{Discounted Amount} = P - D = 12000 - 9000 = 3000 \][/tex]
The discounted amount is Rs. 3,000.
(d) What was the amount that is paid by the tourist at the shop? Calculate it.
The amount paid by the tourist includes the discounted price plus the VAT:
[tex]\[ \text{Amount Paid} = D + \text{VAT} = 9000 + 1170 = 10170 \][/tex]
The amount paid by the tourist at the shop is Rs. 10,170.
### Summary:
- The marked price of the camera: Rs. 15,800
- Rs. 1,170 represents the VAT amount refunded to the tourist.
- The label price of the Khukuri: Rs. 12,000
- The discounted amount: Rs. 3,000
- The amount paid by the tourist at the shop: Rs. 10,170
