X, Y and Z collect stamps. They exchange stamps among themselves according to the following scheme: X gives Y as many stamps Y has and Z as many stamps as Z has. After that, Y gives Z and Z as many stamps as each them has, and then Z gives X and Y as many stamps as each has. If each finally has 64 stamps, with how many stamps does X start?
Answers
Given : X, Y and Z collect stamps. They exchange stamps among themselves according to the following scheme: X gives Y as many stamps Y has and Z as many stamps as Z has.
After that, Y gives Z and X as many stamps as each of them has, and then Z gives X and Y as many stamps as each has.
each finally has 64 stamps,
To Find : how many stamps does X start
Solution:
Lets go reverse :
At end Z gives X and Y as many stamps as each has.
finally Each has 64 stamps
=> Before that X and Y had 32 stamps so that 32 + 32 = 64
and Z had = 64 + (32 + 32) = 128
Z = 128 X = 32 , Y = 32
Before that Y gives Z and X stamps as they have
so Z = 128/2 = 64 and X = 32/2 = 16
and Y had = 32 + (64 + 16) = 112
Hence
X = 16 , Y = 112 Z = 64
Before that X gives Y as many stamps Y has and Z as many stamps as Z has
=> y = 112/2 = 56 , Z = 64/2 = 32
X = 16 + 56 + 32 = 104
X = 104 , Y = 56 , Z = 32
X starts with 104
X Y Z
104 56 32
16 112 64
32 32 128
64 64 64
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