Question

A watch which gains $5$ seconds in $3$ minutes was set right at $7:00$ a.m. In the afternoon of the same day, when the watch indicated quarter past $4$ o'clock, the true time is

• A. $4:00$ p.m.
• B. $4:08$ p.m.
• C. $3:58$ p.m.
• D. $3:52$ p.m.

Answer 1

The correct option is A $4:00$ p.m.

Time from $7:00$ a.m. to $4:15$ p.m.
$=9$ hr $15$ min $=\frac{37}{4}$ hr
Let $x$ be the true number of hours from $7:00$ a.m.
Then, $x+$ gain $=\frac{37}{4}$
gain $=(\frac{5}{3\times 60}\times x)$ hr
$\therefore x+\frac{x}{36}=\frac{37}{4}$
$\Rightarrow x=9$
$\therefore$ The correct time is $9$ hr after $7:00$ a.m. i.e., $4:00$ p.m.