Question

A clock was set right at 2pm it gains 5 seconds in 3 minutes and it indicates 8:30 am the next morning then the true time is

Answer 1

Let the correct time = x a.m.



Note
From 2pm to mid-night = 10 hours
From mid-night to x am = x hours

So, total time from 2 pm to x am =  (10 + x) hours

                                                    = (10 + x)60 minutes

The clock gains 5 seconds every 3 minutes

Total seconds gained = (10 + x)60 x 5/3
   
                                   = 1000 + 100x

If we subtract these gained seconds from 8.30 am, we get the correct time (x)

So;

8.30 - (1000 + 100x) = x

Convert 8.30 and x into seconds, we get

30600 - (1000 + 100x) = 3600x

30600 - 1000 - 100x = 3600x

29600 = 3700x

x = 29600/3700

x = 8

Therefore, the correct time = 8.00 a.m.

PROOF

From 2.00pm to 8.00 am is 18 hours = 1080 minutes

Total seconds gained = 1080 x 5/3 = 1800 seconds

                                                        = 30 minutes

That's why the clock is showing 8.30 am instead of 8.00 a.m.

Answer 2

Solution :-

The clock gains 5 seconds in 3 minutes or 5 seconds in every 180 seconds.

Time passed according to the correct clock = 180 seconds

Time passed according to the faulty clock = 185 seconds

Given : Time indicated according to the faulty clock = 8:30 am next morning

Time passed from 2 pm to 8:30 am next morning = 18 hours 30 minutes

= 1080 minutes + 30 minutes

= 1110 minutes

= 1110*60 

= 66600 seconds

Time elapsed according to the correct clock = (66000*180)/185

⇒ 11988000/185

⇒ 64800 seconds

We shall convert it in hours. = 64800/3600 

= 18 hours

So, 18 hours should have passed according to the correct clock.

Hence, the true time from 2 pm will be = 2 pm + 18 hours

= 8 am next morning

Answer.