Unadjusted clock

Matej was finding out how precisely the tower clock measures time. He came to the conclusion that if no one adjusted it on an ongoing basis, it would show completely exact time once every 200 days.
a) Calculate by how many seconds the time measured by the tower clock differs from the exact time per 1 hour.
b) Calculate after how many days from the setting of the exact time the time on the tower clock will differ from the exact time by 90 minutes. State all the cases that will occur within a year from the setting of the exact time.

Final Answer:

a =  9 s
b =  25 d
c =  13

Step-by-step explanation:

$$\begin{gathered} 24\cdot 200\cdot a=12\cdot 3600 \\ 4800a=43200 \\ a=\frac{43200}{4800}=9 \\ a=9=9\text{s} \end{gathered}$$

$b=\frac{90\cdot 60}{24\cdot a}=\frac{90\cdot 60}{24\cdot 9}=25\text{d}$

$c=\lfloor 365/b-1\rfloor =\lfloor 365/25-1\rfloor =13$

Try another example