Question

At what time between 5.30 and 6 will the hands of the clock be inclined at ${90}^o$?

• A. $45$ min. past 5
• B. $43\frac{5}{11}$ min. past 5
• C. $43\frac{7}{11}$ min. past 5
• D. $40$ min. past 5

Answer 1

Answer: (C)

$43\frac{7}{11}$ min. past 5

At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain $(25+15)=40$ min. spaces.
55 min. spaces are gained in 60 min.
40 min spaces are gained in $\frac{60\times 40}{55}=43\frac{7}{11}$ min.
Therefore, required time is $43\frac{7}{11}$ min. past 5