The price of an article was increased by x%. Later the new price was decreased by x%. If the latest price was ₹1, then what was the original price of the article?

Given:

The price of an article was increased by x%. Later the new price was decreased by x%.

Latest price = ₹1

Calculation:

Let the original price be P. After increasing by x%, the price becomes:

P × (1 + x/100)

After decreasing by x%, the new price becomes:

P × (1 + x/100) × (1 - x/100)

We are given that the latest price = ₹1, so:

P × (1 + x/100) × (1 - x/100) = 1

⇒ P × (1 - x²/100²) = 1

⇒ P = 1 / (1 - x²/100²)

⇒ P = 100² / (100² - x²)

⇒ P = ₹(10000) / ((100 + x)(100 - x))

∴ The correct answer is option (1).