Consider the following statements: 1. Between 3:16 pm and 3:17 pm, both hour hand and minute hand coincide.…
Consider the following statements:
1. Between 3:16 pm and 3:17 pm, both hour hand and minute hand coincide.
2. Between 4:58 pm and 4:59 pm, both minute hand and second hand coincide.
Which of the above statements is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Statement 1: At 3 o'clock the hands are 15 minute-spaces apart; to coincide the minute hand must gain 15 spaces, which takes $(60/55) \times 15 = 180/11 \approx 16.36$ minutes, i.e. the hands coincide at about 3:16:22, which lies between 3:16 and 3:17. Statement 2: At 4:58 the second hand is at 12; within the next minute it will cross the minute hand, so between 4:58 and 4:59 they coincide. Both statements are correct.