At what time between 5:30 and 6 will the hands of a clock be at right angles?
A. $$43\frac{5}{{11}}$$ min. past 5
B. $$43\frac{7}{{11}}$$ min. past 5
C. 40 min. past 5
D. 45 min. past 5
Answer: Option B
Solution(By Examveda Team)
At 5 o'clock, 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
$$\eqalign{ & = \left( {\frac{{60}}{{55}} \times 40} \right){\kern 1pt} {\kern 1pt} \min . \cr & = 43\frac{7}{{11}}{\kern 1pt} {\kern 1pt} \min . \cr & \therefore {\text{Required time}} = 43\frac{7}{{11}}{\kern 1pt} {\kern 1pt} \min .\,{\text{past}}\,5 \cr} $$
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A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
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A. $$59\frac{7}{{12}}$$ min. past 3
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But how do I know that at 5:00 they are 25 min spaces apart
Thanks a lot
Very clearly explained