[5 \dfrac{5}{11} min. p...] At what time between 7 and 8 oclock will the hands of a clock be in the same straight line but, not

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At what time between 7 and 8 oclock will the hands of a clock be in the same straight line but, not together?

5 min. past 7

5$ \dfrac{2}{11} $min. past 7

5$ \dfrac{3}{11} $min. past 7

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

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 oclock, they are 25 min. spaces apart.

$\therefore$ Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

5 min. spaces are gained in$ \left(\dfrac{60}{55} \times 5\right) $min= 5$ \dfrac{5}{11} $min.

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

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