Question

At what time between 4 and 5 o'clock will the hands of a clock be at right angle for the first time?

• A. $9\frac{5}{11}$ min. past 4
• B. $5\frac{5}{11}$ min. past 4
• C. $11\frac{5}{11}$ min. past 4
• D. $9\frac{7}{11}$ min. past 4

Answer 1

Answer: (B)

$5\frac{5}{11}$ min. past 4

If the time is 4 hours and $x$ minutes after 4, 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 = $120+\frac{x}{2}$
Hence, $120+\frac{x}{2}-6x=90$
$30=\frac{11x}{2}$
$x=\frac{60}{11}$
$x=5\frac{5}{11}$ min. past 4