Question

Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I

Answer 1

• 48 years old.

Explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

• (10y + x)/3 + 20 = 10x + y
• (10y + x)/3 = 10x + y - 20
• 10y + x = 3(10x + y - 20)
• 10y + x = 30x + 3y - 60
• 30x - x + 3y - 10y = 60
• 29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

• 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

• 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

If x = 3

• 29*3 - 7y = 60
• 87 - 7y = 60
• 7y = 27
• y = 27/7, discarded as fraction.

If x = 4

• 29*4 - 7y = 60
• 116 - 7y = 60
• 7y = 56
• y = 8

So the age is 48.