Does the time difference between Cairo and Karachi change during the year?

Yes. Because of daylight saving time the gap moves between −3h and −2h.

When is the best time to call Karachi from Cairo?

Between 09:00 and 15:00 in Cairo, which is 11:00 to 17:00 in Karachi.

Cairo is 2h behind Karachi. This gap is not fixed: daylight saving time moves it between −3h and −2h during the year.

Cairo

Egypt

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Karachi

Pakistan

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A 9-to-5 day in each city overlaps for 6h. That is 09:00–15:00 in Cairo, which is 11:00–17:00 in Karachi.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
Karachi · Pakistan	Asia/Karachi	UTC+5

What is the time difference between Cairo and Karachi?: Cairo is 2h behind Karachi. This gap is not fixed: daylight saving time moves it between −3h and −2h during the year.
Does the time difference between Cairo and Karachi change during the year?: Yes. Because of daylight saving time the gap moves between −3h and −2h.
When is the best time to call Karachi from Cairo?: Between 09:00 and 15:00 in Cairo, which is 11:00 to 17:00 in Karachi.