Question

A purely lunar year has 354 days and a solar year has 365 days. By how many days will the lunar calendar fall behind the seasons in 3 years?

Aman's family follows three calendars. At school they use the Gregorian calendar, a solar calendar. His friend Zoya's family uses the Hijri calendar, which has 12 lunar months making about 354 days, with no extra month. Aman's grandmother uses a traditional Indian calendar whose months follow the Moon but which adds an extra month now and then. Zoya says that the month of Ramzan has come in summer, in the rains and in winter during her lifetime, while Aman notes that Diwali always falls in October or November.