Question

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. $50\frac{4}{11}$ min. past $4$
• D. $56\frac{6}{11}$ min. past $4$

Answer 1

The correct option is D $56\frac{6}{11}$ min. past $4$

At $4$ o'clock, the hands of the watch are $20min.$ spaces apart.
To he in opposite directions, they must be $30$ min. spaces apart.
$\therefore$ Minute hand will have to gain $50min.$ spaces.
$55min.$ spaces are gained in $60min.$
$50min.$ spaces are gained in $(\frac{60}{55}\times 50)min.$ or $54\frac{6}{11}min.$
$\therefore$ Required time $=54\frac{6}{11}$ min. past $4$.