A shopkeeper marks an article at ₹x and offers a discount of 60% on it. He sells it for ₹442 after charging VAT of 30% on the discounted price. What is the value of ₹\(x\)?

Given:

Marked price = ₹x

Discount = 60%

Selling price after discount = ₹442 (inclusive of VAT)

VAT = 30% of discounted price

Formula used:

Selling price after discount = Discounted price + VAT

Calculation:

Let the discounted price = (1 - 60/100) × x = 0.4x

VAT = 30% of the discounted price = 30/100 × 0.4x = 0.12x

Selling price = Discounted price + VAT = 0.4x + 0.12x = 0.52x

Given that selling price = ₹442:

⇒ 0.52x = 442

⇒ x = 442 / 0.52 = ₹850

∴ The marked price is ₹850