Q. A person P asks one of his three friends X as to how much money he had. X replied, “If Y given 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 ?

Explanation : 

A person p asks one of his three friends

Initial Conditions:
X has x rupees
Y has y rupees
Z has z rupees

Statement 1 – If Y gives X Rs. 40:
Y’s new amount = Half of Z’s amount
Equation: y – 40 = (1/2)z

Statement 2 – If Z gives X Rs. 40:
All three will have equal amounts
Equation: x + 40 = y = z – 40

Solving the Equations:
1. From first equation: y – 40 = (1/2)z
Therefore: 2y – 80 = z

2. From second equation: x + 40 = y = z – 40
Substituting z: x + 40 = y = (2y – 80) – 40
x + 40 = y = 2y – 120
Therefore: y = 120

Final Values:
X has Rs. 80
Y has Rs. 120
Z has Rs. 160