Question

The sum of the digits of a two-digit number is 9. If nine times the number equals twice the number obtained by reversing its digits, the number is

• A. 27
• B. 36
• C. 18
• D. 81

Hint:

Using options is the fastest way to solve this!
Check Option (C) 18:
Sum of digits: \(1 + 8 = 9\) (Correct).
Reversed number: 81.
\(9 \times 18 = 162\).
\(2 \times 81 = 162\).
They match perfectly! This takes less than 10 seconds.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question is a digit-based word problem from the topic of Linear Equations in Two Variables.
We are given relations regarding a two-digit number and its reversed-digit counterpart. We need to find the original number.

Step 2: Key Formula or Approach:
Let the tens place digit be \(x\) and the units place digit be \(y\).
The original two-digit number can be written in expanded form as:
\[ \text{Original Number} = 10x + y \]
The number obtained by reversing its digits is:
\[ \text{Reversed Number} = 10y + x \]

Step 3: Detailed Explanation:
From the first condition, the sum of the digits is \(9\):
\[ x + y = 9 \quad \text{(Equation 1)} \]
From the second condition, nine times the original number equals twice the reversed number:
\[ 9(10x + y) = 2(10y + x) \]
Expand both sides:
\[ 90x + 9y = 20y + 2x \]
Group the like terms:
\[ 90x - 2x = 20y - 9y \]
\[ 88x = 11y \]
Divide both sides by 11:
\[ y = 8x \quad \text{(Equation 2)} \]
Substitute Equation 2 into Equation 1:
\[ x + 8x = 9 \]
\[ 9x = 9 \implies x = 1 \]
Now, find \(y\):
\[ y = 8(1) = 8 \]
The original number is:
\[ 10x + y = 10(1) + 8 = 18 \]

Step 4: Final Answer:
The original two-digit number is \(18\).