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Sagot :
Certainly! Let's solve this problem step-by-step.
Given:
- The final price after a 10% discount and adding a 13% VAT is Rs. 7,119.
- Discount rate: 10% or 0.10
- Value Added Tax (VAT) rate: 13% or 0.13
We need to find:
(i) Its marked price.
(ii) Its price excluding VAT.
(iii) The discount amount.
(iv) The value added tax amount.
Let's start solving each part:
### (ii) Marked Price (M)
We'll utilize the given final price and understand the relationship with the marked price:
- The marked price is reduced by 10% (discount) and then a 13% VAT is applied.
- Let's denote the marked price by [tex]\( M \)[/tex].
After applying the discount, the price becomes:
[tex]\[ \text{Discounted Price} = M \times (1 - 0.10) = M \times 0.90 \][/tex]
Now, applying the 13% VAT on this discounted price, we get:
[tex]\[ \text{Final Price} = \text{Discounted Price} \times (1 + 0.13) = M \times 0.90 \times 1.13 \][/tex]
But we know the final price is Rs. 7,119:
[tex]\[ 7119 = M \times 0.90 \times 1.13 \][/tex]
Solving for [tex]\( M \)[/tex]:
[tex]\[ M = \frac{7119}{0.90 \times 1.13} \][/tex]
Therefore:
[tex]\[ M = 7000.00 \][/tex]
So, the marked price is Rs. 7000.
### (i) Price Excluding VAT
The price excluding VAT is simply the discounted price before VAT application.
Discounted Price:
[tex]\[ \text{Discounted Price} = M \times 0.90 \][/tex]
[tex]\[ \text{Discounted Price} = 7000 \times 0.90 \][/tex]
[tex]\[ \text{Discounted Price} = 6300.00 \][/tex]
So, the price excluding VAT is Rs. 6300.
### (iii) Discount Amount
The discount amount can be calculated by the difference between the marked price and the discounted price.
Discount Amount:
[tex]\[ \text{Discount Amount} = M - (\text{Discounted Price}) \][/tex]
[tex]\[ \text{Discount Amount} = 7000 - 6300 \][/tex]
[tex]\[ \text{Discount Amount} = 700.00 \][/tex]
So, the discount amount is Rs. 700.
### (iv) Value Added Tax Amount
The VAT amount is the amount added to the discounted price to get the final price.
VAT Amount:
[tex]\[ \text{VAT Amount} = \text{Discounted Price} \times 0.13 \][/tex]
[tex]\[ \text{VAT Amount} = 6300 \times 0.13 \][/tex]
[tex]\[ \text{VAT Amount} = 819.00 \][/tex]
So, the value added tax amount is Rs. 819.
### Summary:
(i) Its marked price: Rs. 7000
(ii) Its price excluding VAT: Rs. 6300
(iii) The discount amount: Rs. 700
(iv) The value added tax amount: Rs. 819
Given:
- The final price after a 10% discount and adding a 13% VAT is Rs. 7,119.
- Discount rate: 10% or 0.10
- Value Added Tax (VAT) rate: 13% or 0.13
We need to find:
(i) Its marked price.
(ii) Its price excluding VAT.
(iii) The discount amount.
(iv) The value added tax amount.
Let's start solving each part:
### (ii) Marked Price (M)
We'll utilize the given final price and understand the relationship with the marked price:
- The marked price is reduced by 10% (discount) and then a 13% VAT is applied.
- Let's denote the marked price by [tex]\( M \)[/tex].
After applying the discount, the price becomes:
[tex]\[ \text{Discounted Price} = M \times (1 - 0.10) = M \times 0.90 \][/tex]
Now, applying the 13% VAT on this discounted price, we get:
[tex]\[ \text{Final Price} = \text{Discounted Price} \times (1 + 0.13) = M \times 0.90 \times 1.13 \][/tex]
But we know the final price is Rs. 7,119:
[tex]\[ 7119 = M \times 0.90 \times 1.13 \][/tex]
Solving for [tex]\( M \)[/tex]:
[tex]\[ M = \frac{7119}{0.90 \times 1.13} \][/tex]
Therefore:
[tex]\[ M = 7000.00 \][/tex]
So, the marked price is Rs. 7000.
### (i) Price Excluding VAT
The price excluding VAT is simply the discounted price before VAT application.
Discounted Price:
[tex]\[ \text{Discounted Price} = M \times 0.90 \][/tex]
[tex]\[ \text{Discounted Price} = 7000 \times 0.90 \][/tex]
[tex]\[ \text{Discounted Price} = 6300.00 \][/tex]
So, the price excluding VAT is Rs. 6300.
### (iii) Discount Amount
The discount amount can be calculated by the difference between the marked price and the discounted price.
Discount Amount:
[tex]\[ \text{Discount Amount} = M - (\text{Discounted Price}) \][/tex]
[tex]\[ \text{Discount Amount} = 7000 - 6300 \][/tex]
[tex]\[ \text{Discount Amount} = 700.00 \][/tex]
So, the discount amount is Rs. 700.
### (iv) Value Added Tax Amount
The VAT amount is the amount added to the discounted price to get the final price.
VAT Amount:
[tex]\[ \text{VAT Amount} = \text{Discounted Price} \times 0.13 \][/tex]
[tex]\[ \text{VAT Amount} = 6300 \times 0.13 \][/tex]
[tex]\[ \text{VAT Amount} = 819.00 \][/tex]
So, the value added tax amount is Rs. 819.
### Summary:
(i) Its marked price: Rs. 7000
(ii) Its price excluding VAT: Rs. 6300
(iii) The discount amount: Rs. 700
(iv) The value added tax amount: Rs. 819
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