Logical Reasoning

Clocks & Calendar

Hard

At what time between 5 : 30 and 6 O'Clock, will the hands of a clock be at right angle ?

45 min past 5

40 min past 5

$43\frac{7}{11}$ min past 5

$43\frac{3}{11}$ min past 5

✅ Correct Option: 3

At 5:00, hour hand is at 150 degrees. For a right angle (90 degrees apart), the minute hand should be at $150 + 90 = 240$ degrees from 12. Minute hand position at $m$ minutes past 5 is $6m$ degrees. Setting up: minute hand gains 5.5 degrees per minute on hour hand. At 5:00 they are 150 degrees apart. Need 90 degrees: $150 - 5.5m = 90$ , so $m = \frac{60}{5.5} = \frac{120}{11} = 10\frac{10}{11}$ (before 5:30, not in range). For 90 degrees with minute ahead: $5.5m - 150 = 90$ , $m = \frac{240}{5.5} = \frac{480}{11} = 43\frac{7}{11}$ .

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Solution

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