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