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At what time between 9 and 10 oclock will the hands of a watch be together?

45 min. past 9
50 min. past 9
49$ \dfrac{1}{11} $min. past 9
48$ \dfrac{2}{11} $min. past 9
Explanation:

To be together between 9 and 10 oclock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in$ \left(\dfrac{60}{55} \times 45\right) $min or 49$ \dfrac{1}{11} $min.

$\therefore$ The hands are together at 49$ \dfrac{1}{11} $min. past 9.

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