Someone who says he was 60 on 2 April could have:
- just turned 60 on 2 April, making his date of birth 2 April 1840
- getting ready to turn 61 on 3 April, making his date of birth 3 April 1839.
Or anywhere in between.
That is assuming an age of 60 on 2 April 1900 was correct.
The accuracy of his age is another story altogether.