Question

The sum of the digits in a two-digit number is 14. If you reverse

and double the original number, and then add the result to the
original number, the sum is 222. Find the original number. Please help me.

Answer 1

The original number is 86.

Explanation:

The only two-digit numbers whose digits sum to 14 are:

• 59
• 68
• 77
• 86
• 95

If we reverse and double the original number:

• 59 reversed is 95 → 95 × 2 = 190
• 68 reversed is 86 → 86 × 2 = 172
• 77 reversed is 77 → 77 × 2 = 154
• 86 reversed is 68 → 68 × 2 = 136
• 95 reversed is 59 → 59 × 2 = 118

If we add the result of reversing and doubling the original number to the original number:

• 59 + 190 = 249
• 68 + 172 = 240
• 77 + 154 = 231
• 86 + 136 = 222
• 95 + 118 = 213

As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.