Given, Ashok remembers that Asha's birhtday comes after 19th, but before 22nd April.
So, according to him, her birthday came at either on 20th or 21st April.
Now, his mother remembers that Asha's birthday comes after 20th, but before 24th April i.e., either on 21st, 22nd or 23rd April.
From the date mentioned by both of them there is only one date which is common i.e., 21st.
Hence, Asha's birthday comes on 21st April.