Given:
Sum of ages of brother and sister = 15
Product of their ages = 54
To find:
How old is the older one between the two of them?
Solution:
Let x be the age of brother and y be the age of sister.
Sum of ages of brother and sister = 15

...(i)
Product of their ages = 54

[Using (i)]


Splitting the middle term, we get




Using zero product property, we get


If
, then using (i), we get


If
, then using (i), we get


Therefore, the age of older one is 9, the age of younger one is 6 and the difference between their ages is 3.