At what time between 5.30 and 6 will the hands of a clock be at right angles?
(a)$43 \frac{5}{11} \mathrm{min}$. past 5
(b)$43 \frac{7}{11} \mathrm{min}$. past 5
(c)40 min. past 5
(d)45 min. past 5
Answer
Answer (as printed): B
Explanation
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 $(25+15)=40 \mathrm{min}$. spaces. 55 min . spaces are gained in 60 min . 40 min . spaces are gained in $\left(\frac{60}{55} \times 40\right) \mathrm{min} .=43 \frac{7}{11} \mathrm{min}$. ∴ Required time $=43 \frac{7}{11} \mathrm{min}$. past 5.