UPSC Prelims 2021 · CSAT

Question 57: Logical Reasoning and Mental Ability

At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other ?

aAt 7:00 hours

bBetween 7:00 hours and 7:05 hours

cAt 7:05 hours

dBetween 7:05 hours and 7:10 hours

AnswerUPSC’s answer is (d).

At 7:00 the hour hand is at 210° and the minute hand at 0°, so they are 210° apart, 30° more than a straight line. The minute hand gains 5.5° a minute on the hour hand, so it needs 30 ÷ 5.5 = 5 5/11 minutes to cut the gap to 180°. The hands are therefore opposite at about 7:05:27, between 7:05 and 7:10. Remember: the minute hand's relative speed over the hour hand is 5.5° per minute; use it to time any target angle.

Why each option is right or wrong

(a) At 7:00 the hands are 210° apart (150° the other way), not 180°.
(b) 5 5/11 minutes is after 7:05, not before it.
(c) At exactly 7:05 the angle is 182.5°, just over 180°.
(d) Right: 180° occurs about 5 5/11 minutes past 7, between 7:05 and 7:10.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.