Does the time difference between Mumbai and Rome change during the year?

Yes. Because of daylight saving time the gap moves between +3h 30m and +4h 30m.

When is the best time to call Rome from Mumbai?

Between 12:30 and 17:00 in Mumbai, which is 09:00 to 13:30 in Rome.

Mumbai is 3h 30m ahead of Rome. This gap is not fixed: daylight saving time moves it between +3h 30m and +4h 30m during the year.

Mumbai

India

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Rome

Italy

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A 9-to-5 day in each city overlaps for 4h 30m. That is 12:30–17:00 in Mumbai, which is 09:00–13:30 in Rome.

City	Time zone	UTC offset
Mumbai · India	Asia/Kolkata	UTC+5:30
Rome · Italy	Europe/Rome	UTC+2

What is the time difference between Mumbai and Rome?: Mumbai is 3h 30m ahead of Rome. This gap is not fixed: daylight saving time moves it between +3h 30m and +4h 30m during the year.
Does the time difference between Mumbai and Rome change during the year?: Yes. Because of daylight saving time the gap moves between +3h 30m and +4h 30m.
When is the best time to call Rome from Mumbai?: Between 12:30 and 17:00 in Mumbai, which is 09:00 to 13:30 in Rome.