Multiple choice

Arjun goes out at some time between 2 o'clock and 3 o'clock and returns between 4 o'clock and 5 o'clock. He notices that the hands of the clock have exactly interchanged their positions. At what time did he go out?

  1. 15 140 143 past 2 o'clock

  2. 20 70 143 past 2 o'clock

  3. 20 140 143 past 2 o'clock

  4. 30 140 143 past 2 o'clock

  5. 40 140 143 past 2 o'clock
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When hands interchange, the time is given by T = 60/143 * (5H + M) minutes past H. For 2 to 3 o'clock, H=2. The formula for interchanged hands is 60/143 * (5H2 + M2) = M1 and 60/143 * (5H1 + M1) = M2. Solving this results in 20 140/143 minutes past 2.

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