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

• Let the amounts held by X, Y, and Z be $x$, $y$, and $z$ respectively.

• From the first condition, if Y gives ₹40 to X, Y's new amount is $y - 40$ and X's is $x + 40$. The statement says Y will have half of Z's amount, so $y - 40 = \frac{1}{2}z$, which simplifies to $2y - z = 80$.

• From the second condition, if Z gives ₹40 to X, Z's new amount is $z - 40$ and X's is $x + 40$. The statement says all three will have equal amounts, so $x + 40 = y = z - 40$.

• From the equality $y = z - 40$, we can express $y$ in terms of $z$: $y = z - 40$.

• Substitute $y = z - 40$ into the first simplified equation $2y - z = 80$: $2(z - 40) - z = 80 \Rightarrow 2z - 80 - z = 80 \Rightarrow z = 160$.

• Now find the other amounts: $y = 160 - 40 = 120$ and $x + 40 = 120 \Rightarrow x = 80$. The total amount is $x + y + z = 80 + 120 + 160 = 360$.