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,…

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?
  1. Rs. 420
  2. Rs. 360
  3. Rs. 300
  4. Rs. 270

Solution

Let X, Y, Z have x, y, z. From 'If Y gives me Rs.40, Y will have half of Z': $y - 40 = z/2$, so $z = 2y - 80$. From 'If Z gives me Rs.40, all three are equal': $x + 40 = y = z - 40$, giving $x = y - 40$ and $z = y + 40$. Combining $2y - 80 = y + 40$ gives $y = 120$, so $x = 80$, $z = 160$. Total = $80 + 120 + 160 = 360$.

Asked in: CSAT 2021

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