A person P asks one of his three friends X as to how much money he had. X replied, "If Y gives me Rs. 40, then Y will have half of as much as Z, but if Z gives me Rs. 40, then three of us will have equal amount." What is the total amount of money that X, Y and Z have?

Let X, Y, and Z be the initial amounts of money X, Y, and Z have, respectively. From the first statement: "If Y gives me (X) Rs. 40, then Y will have half of as much as Z" This means: X' = X + 40 Y' = Y - 40 Z' = Z The condition is Y' = Z' / 2. So, Y - 40 = Z / 2 2(Y - 40) = Z 2Y - 80 = Z (Equation 1) From the second statement: "but if Z gives me (X) Rs. 40, then three of us will have equal amount." This means: X'' = X + 40 Y'' = Y Z'' = Z - 40 The condition is X'' = Y'' = Z''. So, X + 40 = Y = Z - 40 (Equation 2) From Equation 2, we have two relationships: 1. Y = X + 40 => X = Y - 40 2. Y = Z - 40 => Z = Y + 40 Now substitute Z = Y + 40 into Equation 1: 2Y - 80 = Y + 40 2Y - Y = 40 + 80 Y = 120 Now that we have Y = 120, we can find X and Z: X = Y - 40 = 120 - 40 = 80 Z = Y + 40 = 120 + 40 = 160 So, X has Rs. 80, Y has Rs. 120, and Z has Rs. 160. The total amount of money they have is X + Y + Z: Total = 80 + 120 + 160 = 360 Therefore, the total amount of money that X, Y and Z have is Rs. 360. The final answer is B) Rs. 360.