Convert 10 years into months, which is 120 months. So the youngest is 128 months old. 25% of this is 32 months and the oldest is another 9 months older which makes 41 months older than the youngest child.
If the youngest was born in January then 41 months is 3 years and 5 months. If you add 5 months on to January, the eldest must have been born in June.
Answer = June