Answer to Question #89472 in Algebra for Aravind

Question

In 1932 , I was as old as the number formed by the last two digits of my birth year. When I mentioned the interesting coincidence to my grandfather, he surprised me by saying that the same applied to him also. If so find my year of birth and also my grandfather.

Answer 1

It is reasonable to assume that my grandfather was born in the nineteenth century (he was a devout catholic) since I was alive in 1932. Therefore, his age should be a solution of the equation

1932-(1800+y)=y (0<=y<100<=132)

1932-1800-y=y

1932-1800=2y

132=2y

y=66

Because this equation has only one solution, I must be born in the twentieth century. Thus, my age should be a solution of the equation

1932-(1900+x)=x (0<=x<=32<100)

1932-1900-x=x

1932-1900=2x

32=2x

x=16

From these findings, we conclude that my year of birth is 1916, and my grandfather’s year of birth is 1866.