# Total percentage difference of items

If I take say $40\%$ of $X$ to create $Y$, and then $40\%$ off of $Y$ to create $Z$ how do I work out the total percentage taken off of $X$ to get to $Z$?

• Welcome to Math.SE! Can you show us what you have tried? What part of this procedure do you find difficult? – Hrodelbert Sep 30 '15 at 12:09

If you take $40\%$ of $X$ uniformly to create $Y$ and then $40\%$ from $Y$ (which is now $40\%$ $X$) to create $Z$ then you would have $40\%$ of $40\%$ of $X$, which is $0.40\cdot0.40=0.16=16\%$.
If this is not done uniformly, but randomly you will have an upper bound of $16\%$ (that is, $Z$ will be between $0%$ to $16\%$ $X$).
• Why should there be "$Z$ will be between $0$ to $16\%$ of $X$" ? Shouldn't it be just $16\%$ of $X$ because the whole of $Y$ is made from the $40\%$ of $X$. – gamma Sep 30 '15 at 12:25
• If you pick $40\%$ of $Y$ randomly, it might happen that you pick everything from the $60\%$ part of non-$X$. In that case you would have $0\%$ $X$ in $Z$. – Per Sep 30 '15 at 12:26
• It has not been said that part of $Y$ is made from $X$. – gamma Sep 30 '15 at 12:28
• I assumed that $X$ contributes $40\%$ in the creation of $Y$ and not that $Y=0.4\cdot X$. In the latter case you are right, it is exactly $0.16$. – Per Sep 30 '15 at 12:35
• It has not been said that $X, Y \in \mathbb{R}$. – Per Sep 30 '15 at 12:46