Question

At what time between $5:30$ and $6:00$ will the hands of a clock be at right angle?

A. $54\frac{5}{11}$ minutes past $5$

B. $43\frac{7}{11}$ minutes past $5$

C. $63$ minutes past $5$

D. $41$ minutes past $5$

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

At $5$ o’ Clock, the hands are $25$ minute spaces apart. [Since, $12.00$ to $5.00$]

To be at right angle, between $5:30$ and $6$, the minute hand has to gain $(25+15)=40$ minute spaces. [Since, $6.00$ to $9.00$ is $15$ minutes]

$55$ minute spaces are gained in $60$ minutes.

$40$ minute spaces are gained in $\frac{60}{55}\times 40$ minutes.

$=\frac{480}{11}$ minutes.

$=43\frac{7}{11}$ minutes
$\therefore$ The required time $=43\frac{7}{11}$ minutes past $5$