Arvind purchased a wrist watch with 30% discount on the labelled price. He sold it with 40% profit on the price he bought. What was his percent loss on the labelled price ?

Given:

Arvind purchased a wrist watch with 30% discount on the labelled price. He sold it with 40% profit on the price he bought.

Concept:

To determine the percent loss on the labelled price, we need to calculate the effective cost price and selling price in terms of the labelled price.

Formula Used:

If the labelled price is L, the purchase price after discount is:

⇒ Purchase Price = L × (1 - Discount%)

The selling price with profit is:

⇒ Selling Price = Purchase Price × (1 + Profit%)

Percent loss with respect to the labelled price is:

⇒ Percent Loss = [(Labelled Price - Selling Price) / Labelled Price] × 100%

Calculation:

Let the labelled price be L.

Given discount = 30%

⇒ Purchase Price = L × (1 - 0.30)

⇒ Purchase Price = L × 0.70

Given profit = 40%

⇒ Selling Price = Purchase Price × (1 + 0.40)

⇒ Selling Price = L × 0.70 × 1.40

⇒ Selling Price = L × 0.98

Percent loss with respect to the labelled price:

⇒ Percent Loss = [(L - 0.98L) / L] × 100%

⇒ Percent Loss = [0.02L / L] × 100%

⇒ Percent Loss = 2%

∴ The correct answer is option 1.