A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00p.m. on Wednesday, what is the correct time?

Correct Option (1)

To determine the correct time, the total time elapsed and the cumulative gain of the faulty clock must be calculated.

• Calculate Total Elapsed Time:
  • The clock was set right at 8:00 a.m. on Monday.
  • The faulty clock shows 6:00 p.m. on Wednesday.
  • Duration from Monday 8:00 a.m. to Tuesday 8:00 a.m. = 24 hours.
  • Duration from Tuesday 8:00 a.m. to Wednesday 8:00 a.m. = 24 hours.
  • Duration from Wednesday 8:00 a.m. to Wednesday 6:00 p.m. = 10 hours.
  • Total elapsed time = 24 + 24 + 10 = 58 hours.
• Calculate Total Time Gained by the Clock:
  • The clock gains 10 minutes in every 24 hours.
  • Gain per hour = $\frac{10}{24}$ minutes.
  • Total gain in 58 hours = $\frac{10}{24}\times 58$ minutes.
  • Total gain = $\frac{580}{24}=\frac{145}{6}$ minutes.
  • Converting this to minutes and seconds: $\frac{145}{6}$ minutes = 24 minutes and $\frac{1}{6}$ minute.
  • Since 1 minute = 60 seconds, $\frac{1}{6}$ minute = $\frac{1}{6}\times 60$ seconds = 10 seconds.
  • Thus, the clock has gained 24 minutes and 10 seconds over 58 hours.
• Determine the Correct Time:
  • The faulty clock shows 6:00 p.m.
  • To find the correct time, subtract the gained time from the time shown by the faulty clock.
  • Correct time = 6:00:00 p.m. - 0:24:10.
  • Correct time = 5:35:50 p.m.
• Select the Closest Option:
  • Among the given options, 5:36 p.m. is the closest value to 5:35:50 p.m. This implies that for the purpose of selecting the answer from the provided options, the gain is considered approximately 24 minutes, leading to 6:00 p.m. - 24 minutes = 5:36 p.m.

Incorrect Options:

Options 2 (5:30 p.m.), 3 (5:24 p.m.), and 4 (5:18 p.m.) are incorrect because they do not correspond to the calculated gain of 24 minutes and 10 seconds. These options would result from different magnitudes of time gain, which are inconsistent with the clock's specified rate of gaining 10 minutes every 24 hours over the 58-hour period.