Multiple choice

A watch which gains $5$ seconds in $3$ minutes was set right at $7$ a.m. In the afternoon of the same day, when the watch indicated quarter past $4$ o'clock, then the true time is

  1. $4$ p.m.
  2. $59\dfrac {7}{12}$ minutes past $3$
  3. $58\dfrac {7}{11}$ minutes past $3$
  4. $2\dfrac {3}{11}$ minutes past $4$
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A Correct answer
Explanation

The watch gains 5 seconds every 3 minutes. In 1 hour (60 minutes), it gains 5 * 20 = 100 seconds. From 7 a.m. to 4:15 p.m. is 9 hours and 15 minutes (9.25 hours). Total gain = 9.25 * (100/60) minutes = 9.25 * 1.666 = 15.416 minutes. 4:15 minus 15.416 minutes is 4:00 p.m.

AI explanation

Let the actual duration from 7 a.m. to the true time be x minutes. The watch runs at a rate of 185 seconds for every 180 seconds of real time, making the total watch time 185x divided by 180. The watch indicates 9 hours and 15 minutes, which is 555 minutes past 7 a.m. Setting 185x divided by 180 equal to 555 yields x equal to 540 minutes. Adding this 540 minutes (9 hours) to 7 a.m. makes the true time exactly 4 p.m.

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