Henry Ernest Dudeney/Modern Puzzles/18 - A Curious Paradox/Solution

Modern Puzzles by Henry Ernest Dudeney: $18$

A man went into a shop to pay a little bill that he owed.

On placing the money on the counter he found that he had not quite sufficient,

owing to a small purchase that he had thoughtlessly made on the way.

"I am so sorry," he said, "but you see I am a little short.

"Oh, that is all right," replied the tradesman, after looking at the money, "it won't make any difference to me."

"My good man!" exclaimed the customer ...

... etc. etc. ...

"... But really it will not affect my pocket in the slightest."

Can you explain the mystery?

It may come to you in a flash.

The tradesman was certainly correct.

First guess: the small amount difference spans the threshold between tax brackets, which he would have had to pay to the government.

Dudeney explains it in some detail, the gist of which is as follows:

A payment of $\pounds 2$ invoked a cost to the recipient of $1 \oldpence$, leaving him with $\pounds 1 \ 19 \shillings 11 \oldpence$.

Recall:

$1$ pound sterling ($\pounds 1$) is $20$ shilling ($20 \shillings$)

$1$ shilling is $12$ (old) pence ($12 \oldpence$)

The man came to the shop $1 \oldpence$ short, with $\pounds 1 \ 19 \shillings 11 \oldpence$.

At that selling price the tax does not apply.

So paying a penny less is no loss to the seller.

So the initial guess was correct: it was a tax thing.

$\blacksquare$

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $18$. -- A Curious Paradox