Answer: Brian will be 25
Working it out by thinking about the numbers
If Brian's age begins with 1, his father's age should end with 1
Brian's father's age won't end with 1 until Brian is more than 20
If Brian's age begins with 2, his father's age should end with 2
Adding the same number of years to each age
So their ages will be each other's reverses in 11, 22, 33... years time.
Next time is in 11 years, 14 + 11 = 25
Using algebra to find numbers that are each other's reverses and are the correct distance apart
Brian's age written $ab$, Brian's age is $10a+b$
Father's age written $ba$, Father's age is $10b+a$.
$41-14 = 27$ so Brian's father is $27$ years older than Brian.
$$\begin{align}10a+b+27&=10b+a\\
10a+27&=10b+a-b\\
10a-a+27&=10b-b\\
9a+27&=9b\\
a+3&=b\end{align}$$
$a$ |
$b$ |
Brian's age |
Father's age |
1 |
4 |
14 |
41 |
2 |
5 |
25 |
52 |
3 |
6 |
36 |
63 |
etc. |
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