Eid Riddle

Here’s a fun puzzle appropriate for this time of year!

A family has five children. …

• The middle child, Fatimah, was born on Eid al-Fiṭr, and her age is the average age of all five children.
• The age difference between the first child, Ali, and the last child, Husayn, is 10 years.
• The sum of the ages of Muhammad, whose birthday is Eid al-‘Adhā, and Ali, whose birthday is Eid al-Ghadīr, is 20.
• When Husayn was born (on Eid al-Mubāhalah), Muhammad had just turned 4 years old.
• The sum of the ages of all five children (at the end of the lunar year) is 45.

What are the ages of all five children?
And when is Hasan’s birthday?

(All dates and ages are in lunar years, and assume the question is taking place on the last day of the lunar year.)

Gur ntrf bs gur svir puvyqera ner nf sbyybjf: Nyv (guvegrra), Unfna (guvegrra), Sngvznu (avar), Zhunzznq (frira), naq Uhfnla (guerr).

Fvapr Unfna naq Nyv ner gur fnzr ntr ng gur raq bs gur lrne, rvgure gurl jrer obea frireny zbaguf ncneg va gur fnzr yhane lrne, be gurl ner gjvaf. Ohg Nyv, gur byqrfg, jnf obea ng gur raq bs gur yhane lrne, fb gur bayl cbffvovyvgl vf gung Nyv naq Unfna ner gjvaf; guhf, Unfna’f oveguqnl vf nyfb Rvq ny-Tunqve.