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Q43 (CISF/2018) Miscellaneous & General Knowledge › Important Days, Places & Events

How many times in a day are the hour hand and the minute hand of a wall clock straight (i.e., the angle between them is 180°) ?

Explanation

In a 12-hour period, the hour and minute hands of a clock are opposite (at an angle of 180°) exactly 11 times. While one might expect 12 occurrences, the opposition that would occur between 5:00 and 6:00 and between 6:00 and 7:00 happens at exactly 6:00. This overlap reduces the count by one for every 12-hour cycle.

The hands are 180° apart at approximately these times in a 12-hour cycle:

  • 12:32
  • 1:38
  • 2:43
  • 3:49
  • 4:54
  • 6:00
  • 7:05
  • 8:10
  • 9:16
  • 10:21
  • 11:27

Since a full day consists of 24 hours, the hands are straight (180°) a total of 11 × 2 = 22 times.

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SIMILAR QUESTIONS

IAS · 2002 · Q105 Relevance score: 5.92

The time in the wall-clock is 3.25 the acute angle between the hours-hand and the minutes-hand is

IAS · 1997 · Q150 Relevance score: 5.79

The number of times in a day the Hour-hand and the Minute-hand of a clock at right angles is

IAS · 2009 · Q71 Relevance score: 4.93

How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?

A) 16
B) 18
C) 20
D) 22

CAPF · 2025 · Q62 Relevance score: 3.58

A clock is set right at 8:00 AM in the morning. The minute hand and the hour hand of the clock come together after every 65 minutes. What is the actual time when the clock shows 8:00 PM, approximated to the nearest minutes?