Question

The unit digit of a two digit number is 1 more than twice its tens digit. If the digits are reversed, the new number is 45 more than the original number. Find the number.

Answer 1

Given:

• Let the tens digit be (y).
• Let the unit digit be (x).
• Unit digit (x) is 1 more than twice the tens digit (y): x = 2y + 1
• The number is 10y + x.
• The number with digits reversed is 10x + y.
• When digits are reversed, the new number is 45 more than the original: 10x + y = 10y + x + 45.

Step-wise calculation:

1. Substitute (x = 2y + 1) into the equation:

10(2y + 1) + y = 10y + (2y + 1) + 45

2. Simplify both sides:

20y + 10 + y = 10y + 2y + 1 + 45 

21y + 10 = 12y + 46

3. Bring all terms to one side:

21y – 12y = 46 – 10

9y = 36

4. Solve for (y):

y = 4

5. Find (x):

x = 2y + 1

x = 2 × 4 + 1

x = 9

The two-digit number is 10y + x = 10 × 4 + 9 = 49.

The reversed number is 94, which is 45 more than 49, so the conditions are satisfied.

The required number is 49.