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1. 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. $59 \frac{7}{12}$ min. past 3

B. 4 p.m.

C. $58 \frac{7}{11}$ min. past 3

D. $2 \frac{3}{11}$ min. past 4

Solution:

Time from 7 a.m. to 4:15 p.m. = 9 hrs 15 min. =

\frac{37}{4}

hrs
3 min. 5 sec. of this c;ocl = 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} \times \frac{720}{37} \times \frac{37}{4})

hrs. of the correct clock
= 9 hrs. of the correct clock
∴ The correct time is 9 hrs. after 7 a.m. i.e., 4 p.m.

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