Question

If the digits of my present age are reversed then I get the age of my son. If one year ago my age was twice as that of my son. Find my present age.

• A. 63
• B. 73
• C. 37
• D. 36

Answer 1

The Correct Option is B

Let the present age of the man be \(10a + b\), and the present age of the son be \(10b + a\), where \(a\) and \(b\) are the digits of their ages.

Step 1: According to the given condition, one year ago the man’s age was twice the son’s age: 

\[ (10a + b - 1) = 2 \times (10b + a - 1) \]

Step 2: Simplifying the equation:

\[ 10a + b - 1 = 2(10b + a - 1) \]

\[ 10a + b - 1 = 20b + 2a - 2 \]

Step 3: Rearranging the terms:

\[ 10a - 2a = 20b - b + 1 - 2 \]

\[ 8a = 19b - 1 \]

Step 4: Solving the equation for integer values of \(a\) and \(b\), we find:

\[ a = 7, \quad b = 3 \]

Step 5: Therefore, the present age of the man is:

\[ 10a + b = 10 \times 7 + 3 = 73 \text{ years} \]