Henry Ernest Dudeney/Modern Puzzles/79 - Egg Laying/Solution

Modern Puzzles by Henry Ernest Dudeney: $79$

If a hen and a half lays an egg and a half in a day and a half,

how many and a half who lay better by half will lay half a score and a half in a week and a half?

One hen.

Half a score and a half is $10 \tfrac 1 2$.

A week and a half is $10 \tfrac 1 2$ days.

We have that $1 \tfrac 1 2$ hens lay $1 \tfrac 1 2$ eggs in $1 \tfrac 1 2$ days.

Hence $1$ hen lays $1$ egg in $1 \tfrac 1 2$ days.

A hen who lays better by half will lay $1 \tfrac 1 2$ eggs in $1 \tfrac 1 2$ days.

That is, $1$ egg in $1$ day.

Let $n + \dfrac 1 2$ be the number of better-by-half laying hens who lay $10 \tfrac 1 2$ eggs in $10 \tfrac 1 2$ days.

The same number of hens lay $1$ egg in $1$ day.

That is, half a hen and half a hen, or one hen.

$\blacksquare$