Question

A mechanical hand watch which gains $3$ seconds in $4$ minutes was set right at $11:00$ a.m. In the evening of the same day, when the watch indicated $8:00$ p.m., the true time is

• A. $8:53:20$ p.m.
• B. $8:51:20$ p.m.
• C. $8:53:00$ p.m.
• D. $7:53:20$ p.m.

Answer 1

The correct option is A $8:53:20$ p.m.

Time from $11:00$ a.m. to $08:00$ p.m.
$=9$ hr
Let $x$ be the true number of hours from $11:00$ a.m.
Then, $x+$ gain $=9$
Gain $=(\frac{3}{4\times 60}\times x)$ hr
$\therefore x+\frac{x}{80}=9$
$\Rightarrow x=\frac{80}{9}$ hr
$\Rightarrow x=8$ hr $53$ min $20$ sec
$\therefore$ The correct time is $8:53:20$ p.m.