1 hour have 3600 second
Jack's watch gains 10 seconds every hour.
jack's watch will gain 1 hour or 3600 seconds in 3600/10 = 360 hours
that means jack's watch will show 1 hour more than 10:00 am 15 days later (360/24 = 15 days)
Also,
Jose's watch loses 15 seconds every 30 minutes. or 30 seconds per hour
jose's watch will lose 1 hour or 3600 seconds in 3600/30 = 120 hours
that means jose's watch will show 1 hour less than 10:00 am 5 days later (120/24 = 5 days)
or will show 3 hours less than 10:00 am 15 days later.
hence
Today set time = 10:00 am
15 days later, (360 hours later)
Jack's watch will show 11:00 AM and Jose's watch will show 7:00 AM
= Total 360 hours
Another 15 days later, (360 hours later)
Jack's watch will show 12:00 PM and Jose's watch will show 4:00 AM
= Total 720 hours
Another 15 days later, (360 hours later)
Jack's watch will show 13:00 PM and Jose's watch will show 1:00 AM
= Total 1080 hours
Another 15 days later, (360 hours later)
Jack's watch will show 14:00 PM and Jose's watch will show 22:00PM
= Total 1440 hours
Another 15 days later, (360 hours later)
Jack's watch will show 15:00 PM and Jose's watch will show 19:00PM
= Total 1800 hours
Another 15 days later, (360 hours later)
Jack's watch will show 16:00 PM and Jose's watch will show 16:00PM
= Total 2160 hours
So
shreyasharma1206, your question is ambiguous here because the clock needles does meet after 1080 hours but they are showing same time after 2160 hours. kindly rectify the part, what's been asked specifically