Henry Ernest Dudeney/Modern Puzzles/Arithmetical and Algebraical Problems/Clock Puzzles

Henry Ernest Dudeney: Modern Puzzles: Arithmetical and Algebraical Problems

In a dream, I was travelling in a country where they had strange ways of doing things.

One little incident was fresh in my memory when I awakened.

I saw a clock and announced the time as it appeared to be indicated.

but my guide corrected me.

He said, "You are apparently not aware that the minute hand always moves in the opposite direction to the hour hand.

Except for this improvement, our clocks are precisely the same as those you have been accustomed to."

Now, as the hands were exactly together between the hours of $4$ and $5$ o'clock,

and they started together at noon,

what was the real time?

At what time are the two hands of a clock so situated that,

reckoning as minute points past $\textit {XII}$,

one is exactly the square of the distance of the other?

Mrs. Goodheart gave birth to twins.

The clock showed clearly that Tommy was born about an hour later than Freddy.

Mr. Goodheart, who died a few months earlier, had made a will leaving $\pounds 8400$,

and had taken the precaution to provide for the possibility of there being twins.

In such a case the money was to be divided in the following proportions:

two-thirds to the widow,

one-fifth to the first-born,

one-tenth to the other twin,

and one-twelfth to his brother.

Now, what is the exact amount that should be settled on Freddy?