Q. Consider the following statements:
1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.
Which of the above statements is/are correct?
a. 1 only
b. 2 only
c. Both 1 and 2
d. Neither 1 nor 2
Correct Answer: c. Both 1 and 2
Question from UPSC Prelims 2022 CSAT Paper
Explanation :
From statement 1:
At 3 o’clock, the minute hand is 15 minute spaces apart from hour hand.
To be coincident, it must gain 15 minute spaces.
We know that, 55 minutes are gained in 60 minutes.
So, 15 minutes are gained in (60/55) × 15 = 180/11 minutes = 16.36 minutes
Thus, hour hand and minute hand will coincide at 3:16:36, which is between 3:16 pm and 3:17 p.m.
Hence, statement 1 is correct.
From statement 2:
Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide: At any given time, the second hand moves much faster than the minute hand. This means that during any given minute, there will be a moment when both hands coincide.
Thus, both statements 1 and 2 are correct.
