Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together:a)10 (5/11) min. past 8b)10 (8/11) min. past 8c)10 (10/11) min. past 8d)10 (6/11) min. past 8Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Time at which the hands of a clock will be in the same straight line but not together:

To solve this problem, we need to understand the movement of the hour and minute hands of a clock. The hour hand moves 12 times slower than the minute hand. In one hour, the minute hand completes 360 degrees, while the hour hand only completes 30 degrees.

Approach:

1. Let's assume that the minute hand is at 12 and the hour hand is at some position x minutes past 8.
2. The minute hand covers 360 degrees in 60 minutes, so in x minutes, it covers (360/60) * x degrees.
3. The hour hand covers 30 degrees in 60 minutes, so in x minutes, it covers (30/60) * x degrees.
4. Now, we need to find the angle between the minute and hour hand. If the angle is 180 degrees, it means they are in the same straight line but not together.
5. The angle between the hands of the clock is given by the formula: |(360/12) * x - (360/60) * x|.
6. Simplifying the above equation, we get |(30 * x) - (6 * x)| = |24 * x|.
7. We need to find the value of x between 0 and 60 for which |24 * x| = 180.
8. Solving the equation, we get x = 180/24 = 7.5 minutes.
9. Since we need to find the time between 8 and 9 o'clock, we add 7.5 minutes to 8 o'clock.
10. The time at which the hands of the clock will be in the same straight line but not together is 8:07.5 or 10 (10/11) minutes past 8 o'clock.

Therefore, the correct answer is option 'C' 10 (10/11) min. past 8.

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