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
(a)$59 \frac{7}{12} \mathrm{min}$. past 3
(b)4 p.m.
(c)$58 \frac{7}{11} \mathrm{min}$. past 3
(d)$2 \frac{3}{11} \mathrm{min}$. past 4
Answer
Answer (as printed): B
Explanation
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 $=3 \mathrm{min}$. of the correct clock. $\Rightarrow \frac{37}{720} \mathrm{hrs}$ of this clock $=\frac{1}{20} \mathrm{hrs}$ of the correct clock $\Rightarrow \frac{37}{4} \mathrm{hrs}$ of this clock $=\left(\frac{1}{20} \times \frac{720}{37} \times \frac{37}{4}\right) \mathrm{hrs}$ of the correct clock $=9 \mathrm{hrs}$ of the correct clock ∴ The correct time is 9 hrs after 7 a.m., i.e. 4 p.m.