To calculate the year of birth of the boy, we divide the last two digits of the year of birth (1938) by 2, that is 38.2 = 19. So he was born in 1919 and he was 19 years old in 1938. We have divided the number of years elapsed in that century by 2. If we take the previous century also into consideration, the number of years elapsed would be 138 which when divided by 2 gives 69. This number 69 must be the last two digits of the year of birth of grandfather. So he was born in 1869 AD and he was 69 years old in 1938 AD.