Let's solve the given problem step by step:
(i) To find the price of the fan excluding VAT, we need to subtract the VAT amount from the total amount paid by the customer.
Total amount paid with VAT = Rs 3,842
VAT rate = 13%
VAT amount = (VAT rate/100) * Total amount paid
= (13/100) * 3,842
= Rs 499.46
Price of the fan excluding VAT = Total amount paid - VAT amount
= Rs 3,842 - Rs 499.46
= Rs 3,342.54
Therefore, the price of the fan excluding VAT is Rs 3,342.54.
(ii) The marked price of the fan is the original price before any discount is applied. To find it, we need to consider the discount given by the retailer.
Let's assume the marked price of the fan is "M".
Discount rate = 15%
Discount amount = (Discount rate/100) * Marked price
= (15/100) * M
The customer pays the remaining amount after the discount, which is the marked price minus the discount amount:
Amount paid by the customer = Marked price - Discount amount
= M - (15/100) * M
= M - 0.15M
= 0.85M
We know that the customer paid Rs 3,842, so we can equate the amount paid by the customer to Rs 3,842:
0.85M = 3,842
Solving for M:
M = 3,842 / 0.85
= Rs 4,516.47
Therefore, the marked price of the fan is Rs 4,516.47.
(iii) The discount amount is the difference between the marked price and the amount paid by the customer:
Discount amount = Marked price - Amount paid by the customer
= Rs 4,516.47 - Rs 3,842
= Rs 674.47
Therefore, the discount amount is Rs 674.47.
(iv) The amount of Value Added Tax (VAT) is given as 13% of the total amount paid:
VAT rate = 13%
Total amount paid = Rs 3,842
VAT amount = (VAT rate/100) * Total amount paid
= (13/100) * 3,842
= Rs 499.46
Therefore, the amount of Value Added Tax (VAT) is Rs 499.46.