Multiple choice

A and B started a business with a total capital of Rs. 30,000. At the end of the year, they shared the profit in the ratio of their investments. If their capitals were interchanged, then A would have received 175% more than what he actually received. Find out the capital of B.

  1. Rs. 20,000

  2. Rs. 22,000

  3. Rs. 21,000

  4. Rs. 23,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A's capital be x, B's be 30000-x. Profit ratio = x : (30000-x). If interchanged, ratio = (30000-x) : x. A's new profit = (30000-x)/30000 * Total_Profit. A's old profit = x/30000 * Total_Profit. New = 2.75 * Old. (30000-x) = 2.75x. 30000 = 3.75x. x = 8000. B = 30000 - 8000 = 22000.

AI explanation

Let the capital of A be x and the capital of B be (30000 minus x). Their actual profits are in the ratio of x to (30000 minus x), so A's actual profit fraction is x divided by 30000. If the capitals were interchanged, A's new profit fraction would be (30000 minus x) divided by 30000, and this new amount is 275 percent of his actual profit. Setting up the equation, (30000 minus x) divided by x equals 2.75, which simplifies to 30000 minus x equals 2.75x, meaning 30000 equals 3.75x. Solving for x gives A's capital as 8000, making B's capital 30000 minus 8000 to equal 22000.

Keep practicing — related questions