Question

At what time are the hands of a clock together between 5 O'clock and 6 O'clock?

• A. $33\frac{3}{11}$ minutes past 5
• B. $28\frac{3}{11}$ minutes past 5
• C. $27\frac{3}{11}$ minutes past 5
• D. $26\frac{3}{11}$ minutes past 5

Answer 1

Answer: (C)

$27\frac{3}{11}$ minutes past 5

If the time is 5 hours and $x$ minutes after 5, when the two hands of the clock are same, then the angle formed by minute hand is: $\frac{x}{60}\times 360=6x$
The hour hand moves $\frac{1}{2}$ degree each minute, then angle traced by hour hand is = $150+\frac{x}{2}$
Hence, $6x=150+\frac{x}{2}$
$150=\frac{11x}{2}$
$x=\frac{300}{11}$
$x=27\frac{3}{11}$ min. past 5