[54 \dfrac{6}{11} min. ...] At what time between 4 and 5 oclock will the hands of a watch point in opposite directions?

For Competitive Exams

At what time between 4 and 5 oclock will the hands of a watch point in opposite directions?

45 min. past 4

40 min. past 4

50$ \dfrac{4}{11} $min. past 4

54$ \dfrac{6}{11} $min. past 4

Explanation:

At 4 oclock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

$\therefore$ Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in$ \left(\dfrac{60}{55} \times 50\right)$min. or 54$ \dfrac{6}{11} $min.

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