Henry Ernest Dudeney/Modern Puzzles/15 - Sawing Logs/Solution

Modern Puzzles by Henry Ernest Dudeney: $15$

"Your charge," said Mr. Grigsby, "was $30$ shillings for sawing up $3$ cords of wood made up of logs $3$ feet long,

each log to be cut into pieces $1$ foot in length."

"That is so," the man replied.

"Well, here are $4$ cords of logs, all of the same thickness as before,

only they are in $6$-feet lengths, instead of $3$ feet.

What will your charge be for cutting them all up into similar $1$-foot lengths?"

It is curious that they could not at once agree as to the fair price for the job.

What does the reader think the charge ought to be?

The workman charges for the number of cuts per log.

A cord is a unit of volume.

$4$ cords of $6$-foot logs is the same number of logs as $2$ cords of $3$-foot logs.

The key point is that:

it takes $2$ cuts to cut a $3$-foot log into $1$-foot pieces

but:

it takes $5$ cuts to cut a $6$-foot log into $1$-foot pieces.

So the workman should charge:

$30 \times \dfrac 2 3 \times \dfrac 5 2 = 50 \shillings$

$\blacksquare$