Henry Ernest Dudeney/Modern Puzzles/88 - Correcting an Error/Solution

Modern Puzzles by Henry Ernest Dudeney: $88$

Hermione was given a certain number to multiply by $409$,

but she made a blunder that is very common with mudbloods when learning the elements of simple arithmetic:

she placed the first figure of her product by $4$ below the second figure from the right instead of below the third.

We have all done that as youngsters (speak for yourself, Harry, old boy) when there has happened to be a $0$ in the multiplier.

The result of Hermione's mistake was that her answer was wrong by $328,320$, entirely in consequence of that little slip.

Now, what was the multiplicand?

$912$

Let $x$ be the multiplicand.

Misplacing the partial product as described causes the multiplier to be $49$ and not $409$.

Hence we have:

$409 x - 49 x = 328320$

which after some simple algebra gives:

$x = 912$

Easy peasy lemon squeezy.

$\blacksquare$