Assalamu alaikum.Thank you for question no.2103232.But,1. how can the problem of Eid being celebrated in 2 days in 2 adjacent towns hardly 10 to 20 kilometers apart be solved?2.Once sighted till how much distance is it valid?According to Imam Nawavi(Allah's mercy on him)the distance is upto travel time for Kasr prayer.Is it till valid now?Was Salam.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

All the Muslims should fear Allaah and avoid scattering into sects as this is an evil act. They are all required to hold fast to the rope of Allaah (Islam), and the residents of one country which has one sighting location are obliged to fast at the same time and celebrate the 'Eed at the same time and slaughter at the same time [i.e. on the same day], either by the confirmation of the sighting of the moon or by completing Sha'baan 30 days. However, they are not obliged to coincide with another country which differs with them with regard to the sighting location. 

The distance which the questioner mentioned between the two cities is not a big distance, so they are all obliged to fast on the same day according to the sighting of the moon or after completing Sha'baan 30 days, but this should be after endeavouring to see the moon on the night of the 29th of Sha'baan.

An-Nawawi said: 'If the moon is seen in a country and is not seen in another country, then the ruling is that they are like one country if both of them are close to each other, and the people of the second country are obliged to fast without any difference of opinion.'

Moreover, the scholars only differed in regard to the countries which are far from each other, and what should be taken into account in relation to them.

What the questioner mentioned about An-Nawawi that what should be taken into account in his view is the distance of shortening the prayer is not correct. Rather, Imaam An-Nawawi is of the view that the difference in sighting locations should be taken into account.

So, when there is only one sighting location, all the other countries are obliged to fast if one country has sighted the moon. But if there is a difference in the sighting location, then the other countries are not obliged to fast according to the sighting of one country. Indeed Imaam classified the view of the scholars who are of the opinion that the distance of shortening the prayer should be taken into account, as weak, as he said: 'This view is weak because the crescent has nothing to do with the distance of shortening the prayer, so the most preponderant opinion is to take into consideration the sighting location as already discussed.'

For more benefit, please refer to Fataawa 81595 and 85698.