Henry Ernest Dudeney/Puzzles and Curious Problems/37 - A Wages Paradox/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $37$

A Wages Paradox

"I want a rise, sir," said the office-boy.

"That's nonsense," said the employer.

"If I give you a rise you will really be getting less wages per week than you are getting now."

The boy pondered over this, but was unable to see how such a thing could happen.

Can you explain it?

Solution

The unconvincing solution given by Dudeney is as follows.

The office-boy was earning $\pounds 3, 10 \shillings$ per week.

This was to be increased to $\pounds 200$ per annum, paid monthly by cheque.

It is decided that the first month of the new arrangement was that he was to continue to be paid week by week.

There are $5$ weeks in the first month.

As the total paid in the first month is $\pounds 16, 13 \shillings 4 \oldpence$, it follows that the weekly sum paid on each of the five pay days would be $\pounds 3, 6 \shillings 8 \oldpence$ only.

This is less by $3 \shillings 4 \oldpence$ than under the old arrangement.

So he will receive less per week, though earning more per annum.

This state of affairs happens, of course, only when there are $5$ paydays in the month.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $37$. -- A Wages Paradox