I have been reading Ray's Intellectual Arithmetic and I stumbled upon the following problem:
What is the time in the afternoon, when the time past noon is equal to $1/5$ of the time past midnight?
The solution goes like this:
Let $5/5$ be the whole time. The time past noon is $1/5$. From midnight to noon is $4/5$. Then $4/5 = 12$. Therefore $1/5$ is $3$ o'clock in the afternoon.
But $4$ o'clock is also $1/5$ of some time after midnight. Is this problem ambiguous?
I interpret the question as currently the time is $x$.
Noon is the time corresponding to $12:00$ hours and midnight is the time corresponding to $00:00$ hours
The time past noon is $x-12$ and the time past midnight is $x-0$.
$$x-12 = \frac15 ( x-0)$$
$$\frac{4x}5=12$$
$$x=15$$
That is $x$ is $15:00$ hours, which corresponds to $3pm$.
Remark about $4$ O' clock is some times after midnight. Let that time be $
$$16-12=\frac15(16-y)$$
$$y=-4$$
There is no time after midnight that make the equation holds unless you are measuring from $8pm$ the previous day.