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 the amount of money with X, Y and Z be x, y and z. As per the question, If Y gives me Rs. 40, then Y will have half of as much as Z. That is, y – 40 = z/2 Or z = 2y - 80 ……(i) If Z gives me Rs. 40, then three of us will have equal amount. That is, x + 40 = y = z – 40 So, x = y – 40 And z = y + 40 ……(ii) Using statements (i) and (ii), we get: 2y – 80 = y + 40 Or y = 120 So, x = y – 40 = 120 – 40 = 80 And z = y + 40 = 120 + 40 = 160 So, money with X, Y and Z will be Rs. 80, Rs. 120, and Rs. 160. Total amount of money with X, Y and Z = x + y + z = 80 + 120 + 160 = Rs. 360