Vinay sold a watch in ₹ 75. He gets profit as the same s cost price of the…

Step-by-Step Solution

1. Define the variables:

   • Cost Price = x

   • Profit Percentage = x%

   • Selling Price (SP) = Rs. 75

2. Set up the equation:

   • Profit = (Profit Percentage / 100) * Cost Price

   • Profit = (x / 100) * x = x^2 / 100

   • Selling Price = Cost Price + Profit

   • 75 = x + x^2 / 100

3. Solve the quadratic equation:

   • Multiply the entire equation by 100 to clear the denominator: 7500 = 100x + x^2 x^2 + 100x - 7500 = 0

4. Factor the quadratic equation:

   • We need two numbers that multiply to -7500 and add to 100. These numbers are 150 and -50.

   • (x + 150)(x - 50) = 0

   • x = -150 or x = 50.

   • Since cost price cannot be negative, x = 50.