[43 \dfrac{7}{11} min. ...] At what time between 5.30 and 6 will the hands of a clock be at right angles?

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At what time between 5.30 and 6 will the hands of a clock be at right angles?

43$ \dfrac{5}{11} $min. past 5

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

40 min. past 5

45 min. past 5

Explanation:

At 5 oclock, 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$ \left(\dfrac{60}{55} \times 40\right) $min=43$ \dfrac{7}{11} $min.

$\therefore$ Required time = 43$ \dfrac{7}{11} $min. past 5.

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