Henry Ernest Dudeney/Puzzles and Curious Problems/353 - The Three Sugar Basins/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $353$

Three basins each contain the same number of lumps of sugar,

and nine cups are empty.

If we transfer to each cup one-eighteenth of the number of lumps that each basin contains,

we then find that each basin holds $12$ more lumps than each of the cups.

How many lumps are there in each basin before they are removed?

$36$

Let $n$ be the number of lumps each basin contains before starting.

Each sugar bowl transfers a total of $9 \times \dfrac n {18} = \dfrac n 2$ lumps to the teacups.

So after this transaction, each sugar bowl contains $n - \dfrac n 2 = \dfrac n 2$ lumps.

Each teacup then contains a total of $3 \times \dfrac n {18} = \dfrac n 6$ lumps.

Hence:

$\dfrac n 2 = \dfrac n 6 + 12$

which after algebra leads us to:

$n = 36$

$\blacksquare$