Correct Answer - Option 2 : 3:00 p.m.
We are going to check by option
Clock gains 5 seconds for every 3 minutes
So, 100 seconds for every 60 minutes
Wrong clock shows time as 3:15, so in actual time will be less than 3:15
Thus option (a) and option (d) is not possible
From option (b),
Let 3:00 be the time in accurate clock
Total time duration = 9 hours
Clock gains in 9 hour = 9 × 100 seconds = 15 minutes
From option (b), we get the time 3:15.
Clock gains 5 second in 3 minutes.
Now total time = 6 a.m. to 3:15 p.m. = 9 hours 15 minutes.
⇒ 9 hours 15 minutes = 9 × 60 + 15 minutes
⇒ (540 + 15) minutes
⇒ 555 minutes
∴ Total time gained by clock
So, 3 minutes → 5 sec.
1 minutes → 5 sec\3
∴ 555 minutes → 5 sec × 555\3 = 925 sec.
⇒ 925 sec. = 15 mint. 25 sec.
So, In accurate the clock shows = 3:15 - 15 mint. 25 sec = 3:00 (25 sec)
Hence,
3:00 p.m. is the right time.