At what time between $5$ O'clock & $5 : 30$ will the hands of a clock be at right angle?
- $\displaystyle 10 \frac{10}{11}$ minutes past $5$.
- $\displaystyle 11 \frac{5}{11}$ minutes past $5$.
- $\displaystyle 9 \frac{10}{11}$ minutes past $5$.
- $\displaystyle 10 \frac{9}{11}$ minutes past $5$.
Reveal answer
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A
Correct answer
Explanation
At 5 o'clock, the minute hand is at 12 and the hour hand is at 5 (25 minutes apart). For a 90-degree angle, the hands must be 15 minutes apart. The minute hand must gain 25 - 15 = 10 minutes. Time = 10 * (60/55) = 10 * 12/11 = 120/11 = 10 10/11 minutes past 5.
AI explanation
Using the standard formula for right angles, we set the equation as 5.5 times the minutes minus 30 times the hour equal to 90 degrees. For 5 o'clock, this gives the equation 5.5M - 150 = 90. Solving for M, we add 150 to 90 to get 240, and dividing by 5.5 yields 10 10/11 minutes past 5.