student asked in Science & MathematicsMathematics · 2 months ago

# A simple solution to a percentage problem. Or is it?

A man is 6ft tall and his son is a similar solid 5ft tall; they have suits of the same style and cloth. If the weight of the man’s suit is k per cent of his weight, find the weight of the boy’s suit as a percentage of the boy’s weight. (Assume father and son have same density.) What general conclusion can be drawn about the density of cloth suitable for adults and children.

Now, solution gives 6/5 k%, which to me appears to be the ratio of the man’s height to his son’s multiplied by the original percentage of man’s weight. Although I’m sure the author is correct, this doesn’t sit well with me. It doesn’t seem to indicate anything about, for instance, the ratio of volumes of similar figures being the cube of the scale etc. If there is some short cut here that I’m missing then I’m not sure what it is. I would like to know if there is some general rule I’m missing that can derive the correct answer quickly.

As always any help to cure my inability to see the woods for the trees (I think that’s right) would be greatly appreciated.