Finding a Two Digit Number

Video Explanation

Question

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. Find the number.

Solution

Step 1: Assume Digits

Let tens digit = \(x\), units digit = \(y\)

Number = \(10x + y\)

Step 2: Form Equations

From sum of digits:

\[ x + y = 9 \quad (1) \]

From reversing condition:

\[ 10x + y + 27 = 10y + x \]

\[ 9x – 9y = -27 \]

\[ x – y = -3 \quad (2) \]

Step 3: Solve Equations

From (1) and (2):

\[ x + y = 9 \]

\[ x – y = -3 \]

Add both:

\[ 2x = 6 \Rightarrow x = 3 \]

Substitute into (1):

\[ 3 + y = 9 \Rightarrow y = 6 \]

Step 4: Form Number

\[ \text{Number} = 10x + y = 36 \]

Final Answer

\[ \text{The required number is } 36. \]