Greek Anthology Book XIV: 7. - Problem/Variant/Mistake

Source Work

 * The Puzzles:
 * Light Reflected off a Mirror: $20$
 * Solution
 * Solution

Mistake

 * $A$ and $B$ together can do a piece of work in $6$ days, $B$ and $C$ together in $20$ days, $C$ and $A$ together in $7 \frac 1 2$ days. How long will each require separately to do the same work?

The solution is given as:
 * $A$, $B$ and $C$ do the whole job in $10$, $15$ and $30$ days respectively.

Correction
With the numbers given, the results are actually:
 * $A$, $B$ and $C$ do the whole job in $8$, $24$ and $120$ days respectively.

For the given solution to be correct, it would be necessary for the question to have been:


 * $A$ and $B$ together can do a piece of work in $6$ days, $B$ and $C$ together in $10$ days, $C$ and $A$ together in $7 \frac 1 2$ days. How long will each require separately to do the same work?

(Emphasis added.)

One of the following things has happened:


 * $(1): \quad$ There is an error in the source work, and has reported it as it has been printed.


 * $(2): \quad$ The source work is correct, but a typo has been introduced into the question when it was entered into.

It has not been possible to check the source work by  to determine which is the case.