Angle traced by the hour hand in 6 hours =$ \left(\dfrac{360}{12} \times 6\right) ^\circ$ = $180^\circ$.
Angle traced by hour hand in$ \dfrac{125}{12} $hrs =$\left(\dfrac{360}{12} \times \dfrac{125}{12}\right)^\circ$= 312$ \dfrac{1}{2}^\circ$.
Angle traced by minute hand in 25 min =$ \left(\dfrac{360}{60} \times 25\right)^\circ $= 150$^\circ$.
$\therefore$ Reflex $\times$ angle = $360^\circ$ -$ \left(312\dfrac{1}{2} - 150\right)^\circ$= 360$^\circ$ - 162$ \dfrac{1}{2}^\circ $= 197$ \dfrac{1}{2} $.
Angle traced by hour hand in 12 hrs = 360$^\circ$
Angle traced by hour hand in 5 hrs 10 min. i.e.,$\dfrac{31}{6}$ hrs =$\left(\dfrac{360}{12} \times \dfrac{31}{6}\right) ^\circ$=155$^\circ$
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =$ \dfrac{37}{4} $hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
$\Rightarrow \dfrac{37}{720} $hrs of this clock =$ \dfrac{1}{20} $hrs of the correct clock.
$\Rightarrow \dfrac{37}{4} $hrs of this clock =$\dfrac{1}{20} \times\dfrac{720}{37} \times \dfrac{37}{4}$hrs of the correct clock.
= 9 hrs of the correct clock.
$\therefore$ The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
60 min. spaces are covered in$ \left(\dfrac{60}{55} \times 60\right) $min.= 65$ \dfrac{5}{11} $min.
Loss in 64 min. =$ \left(65\dfrac{5}{11} - 64\right) $=$ \dfrac{16}{11} $min.
Loss in 24 hrs =$ \left(\dfrac{16}{11} \times\dfrac{1}{64} \times 24 \times 60\right) $min.=32$ \dfrac{8}{11} $min.