Henry Ernest Dudeney/Puzzles and Curious Problems/286 - Unlucky Breakdowns/Solution

by : $286$

 * Unlucky Breakdowns

Solution
There were $900$ people, all travelling in $100$ wagons, $9$ to a wagon.

Then they were down to $90$ wagons, in which they travelled $10$ to a wagon.

Then they were down to $75$ wagons, in which they travelled $12$ to a wagon.

Proof
Let $P$ be the number of people going on the outing.

Let $W$ be the number of wagons.

Let $n$ be the number of people per wagon who started out.

We have: