Question

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 o'clock, the true time is ?

Answer 1

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = $\frac{37}{4}$ hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
=>$\frac{37}{720}$ hrs of this clock = $\frac{1}{20}$ hrs of the correct clock.
=>$\frac{37}{4}$ hrs of this clock = $\frac{1}{20}* \frac{720}{37}* \frac{37}{4}$ hrs of the correct clock.
= 9 hrs of the correct clock.
Thus, the correct time is 9hrs after 7 a.m. i.e. 4 p.m.

Answer 2

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =  hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
=> hrs of this clock =  hrs of the correct clock.
=> hrs of this clock =  hrs of the correct clock.
= 9 hrs of the correct clock.
Thus, the correct time is 9hrs after 7 a.m. i.e. 4 p.m.