Ketan sold 151 chairs and had a gain equal to the selling price of 51 chairs. What is his profit percentage?

Given:

Ketan sold 151 chairs and had a gain equal to the selling price of 51 chairs.

Formula used:

Profit Percentage = \(\frac{\text{Profit}}{\text{Cost Price}} \times 100\)

Profit = Selling Price of 51 chairs

Cost Price = Selling Price of 151 chairs - Profit

Calculation:

Selling Price of 151 chairs = S

Profit = Selling Price of 51 chairs = \(\frac{51}{151} \times S\)

Cost Price = Selling Price - Profit

⇒ Cost Price = \(\text{S} - \frac{51}{151} \times S\)

⇒ Cost Price = \(\frac{151S - 51S}{151}\)

⇒ Cost Price = \(\frac{100S}{151}\)

Profit Percentage = \(\frac{\text{Profit}}{\text{Cost Price}} \times 100\)

⇒ Profit Percentage = \(\frac{\frac{51}{151} \times S}{\frac{100S}{151}} \times 100\)

⇒ Profit Percentage = \(\frac{51}{100} \times 100\)

⇒ Profit Percentage = 51%

∴ The correct answer is option (4).