When does a parent become double a child’s age?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

02 January 2022

Writing from Arusha in Tanzania, Elly Manjale says: I was born in 1951 and my last-born daughter was born in 1991. I recently celebrated my 70th birthday as she celebrated her 30th birthday. As we were pondering our ages my daughter pointed to the fact that in 10 years’ time (2031) I will be 80 an age that will be double hers - 40. The question is - how comes that my age will be double hers in 2031 and not in 2021 when all other things have remained the same?”

Let’s start counting from 1992 – a year after Manjale’s daughter was born. In that year, he celebrated his 41^st birthday while she celebrated her first. Therefore, he was 41 times her age. The following year, he turned 42 and she was 2 years old.

Therefore, in 1993, he was 21 times her age. In just one year, the ratio of his age to hers has almost halved from 41 to 21. Similarly, in 1994, the father celebrated his 43^rd birthday while the daughter turned 3; now the ration of their ages was 43 divided by 3 which is about 14 times.

Clearly, with every passing year, the ratio of their ages reduces even though each one of them is gaining the same time period of 12 months. This progression continues “for ever” – or until one of them dies. Therefore, a year must come when the ratio of the age of father to that of daughter is exactly two. When that year is passed, the ratio will continue reducing.

The question then is, at what time is a parent double the age of their child? Well, since every person gains one year annually, it is easy to see that in the year that the child turns the age the parent was when it was born, then the parent will be twice the child’s age.

In the case of Manjale, he was 40 when his daughter was born; so, when the daughter turns 40, he will also have increased his age by 40 years. That is, he will have doubled his age. Thus, he will be double the daughter’s age.

We may ask another question: assuming that the two don’t die, is there a time when the ratio of their ages will be 1? The answer, obviously is no. The reason is that the father will always be 40 years older than the daughter.