Daily Puzzle - Jun 04 

Workings

Hint
What's a mathematical way to describe placing a 9 at the beginning?

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (e.g. 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (e.g. 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 - 36 = 40k - k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore k = 23,076.

Double-Checking
923,076 = 4 x 230,769. This confirms the answer.