Question
At what time between 9 and 10 o'clock will the hands of a watch be together?
Answer: Option C
To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
45 min. spaces are gained in
$$\left( {\frac{{60}}{{55}} \times 45} \right){\text{min}}{\text{.}}{\kern 1pt} \,{\text{or}}{\kern 1pt} \,49\frac{1}{{11}}{\kern 1pt} {\text{min}}.$$
∴ The hands are together at $$49\frac{1}{{11}}$$ min. past 9
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To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
45 min. spaces are gained in
$$\left( {\frac{{60}}{{55}} \times 45} \right){\text{min}}{\text{.}}{\kern 1pt} \,{\text{or}}{\kern 1pt} \,49\frac{1}{{11}}{\kern 1pt} {\text{min}}.$$
∴ The hands are together at $$49\frac{1}{{11}}$$ min. past 9
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