The profit percent gained if an object is sold at Rs 464 is equals to the loss…

Step-by-Step Solution

When an object is sold at two different prices, and the profit percentage at the higher price is equal to the loss percentage at the lower price, the cost price (CP) is simply the average of the two selling prices.

1. Define the variables:

   • Let CP be the cost price.

   • Profit at Rs. 464 = CP * Profit%

   • Loss at Rs. 436 = CP * Loss%

   • Since Profit% = Loss%, the numerical profit amount equals the numerical loss amount.

2. Set up the equation:

   • Profit = Selling Price (Higher) - CP = 464 - CP

   • Loss = CP - Selling Price (Lower) = CP - 436

   • Setting them equal: 464 - CP = CP - 436

3. Solve for CP:

   • 464 + 436 = 2 * CP

   • 900 = 2 * CP

   • CP = 900 / 2 = 450