At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
(a)45 min. past 4
(b)40 min. past 4
(c)$50 \frac{4}{11} \mathrm{min}$. past 4
(d)$54 \frac{6}{11} \mathrm{min}$. past 4
Answer
Answer (as printed): D
Explanation
At 4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30 min. spaces apart. ∴ Minute hand will have to gain 50 min . spaces. 55 min. spaces are gained in 60 min. 50 min . spaces are gained in $\left(\frac{60}{55} \times 50\right) \mathrm{min}$. or $54 \frac{6}{11} \mathrm{min}$. ∴ Required time $=54 \frac{6}{11} \mathrm{min}$. past 4.