A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 oclock, the true time is:
59$ \dfrac{7}{12} $min. past 3
4 p.m.
58$ \dfrac{7}{11} $min. past 3
2$ \dfrac{3}{11} $min. past 4
Explanation:
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =$ \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.