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:

• A. $59\frac{7}{12}$ min. pase $3$
• B. $4$ p.m.
• C. $58\frac{7}{11}$ min. past $3$
• D. $2\frac{3}{11}$ min. past $4$

Answer 1

Answer: (B)

$4$ p.m.

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