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 ?

Correct Answer: (B) ₹ 360

If Z gives ₹ 40 to X, all three have an equal amount $E$, so $y = E$, $x = E - 40$, and $z = E + 40$. Total money is $x + y + z = 3E$. If Y gives ₹ 40 to X, Y has $y - 40 = E - 40$ while Z has $z = E + 40$. We are given $E - 40 =$$\frac{1}{2}$(E + 40), which solves to $\frac{1}{2}E=60⟹E=120$$\frac{1}{2}$E = 60 $\implies$ E = 120. Thus, total money is $3$$\times$ 120 = $\text{₹ }$ 360.