A clock gains 5 seconds for every 3 minutes. If the clock started working at 6 a.m. in the morning, then what will the time in the accurate clock when

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A clock gains 5 seconds for every 3 minutes. If the clock started working at 6 a.m. in the morning, then what will the time in the accurate clock when wrong clock showed 3:15 p.m. on the same day?
1. 4:00 p.m.
2. 3:00 p.m.
3. 2:45 p.m.
4. 3:30 p.m.

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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.