
At what time between 10 O’ clock and 11 O’ close are the two hands of the clock symmetric with respect to the vertical line (give the answer to the nearest second)?
A) 10h9m13s
B) 10h9m14s
C) 10h9m22s
D) 10h9m50s
Answer
474.6k+ views
Hint: In this question we have to find the minutes after 10 hours, at which the hands of the clock become symmetric. To find this first we are going to find minutes. For this we are going to equate two terms and after adding minutes to hours we will get the final answer.
Complete step by step solution:
After x minutes the two hands of the clock become symmetric to each other.
As we already know that the ratio of angular speed of hour to minute hand is .
If the minute hand moves by x minute distance, the hour hand will move by minute distance.
Now to find the value of x, we will equate with .
Hence, from the above calculation we have found out the value of x or the value of minutes . Hence the time at which two hands of the clock will be symmetric is .
Hence option (C) is correct.
Note: The ratio of angular speed of hour hand and minute hand is . Now, we are going to discuss how we get this ratio. As we know that the minute hand of the clock covers in 60 minutes. The hour hand of a clock covers in 60 minutes. We can say it in other way that the minute hand of the clock covers and the hour hand of the clock covers . If we find the ratio of the angular speed of hour to minute hands, it comes out to be . This information of the ratio of angular speed is must to solve such problems.
Complete step by step solution:
After x minutes the two hands of the clock become symmetric to each other.
As we already know that the ratio of angular speed of hour to minute hand is
If the minute hand moves by x minute distance, the hour hand will move by
Now to find the value of x, we will equate
Hence, from the above calculation we have found out the value of x or the value of minutes
Hence option (C) is correct.
Note: The ratio of angular speed of hour hand and minute hand is
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