Henry Ernest Dudeney/Puzzles and Curious Problems/114 - Elementary Arithmetic/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $114$

If a quarter of twenty is four, what would a third of ten be?

$2 \tfrac 2 3$

According to Dudeney, this is:

merely a sum in simple proportion:

If $5$ be $4$, then:

$3 \tfrac 1 3$ is $3 \tfrac 1 3 \times \dfrac 4 5 = \dfrac {10 \times 4} {3 \times 5} = 2 \tfrac 2 3$

$\blacksquare$

This is the kind of question that was very popular in Venice and elsewhere about the middle of the sixteenth century.

Nicola Fontana, generally known as "Tartaglia" (the stammerer) was largely responsible for the invention.