In a two-digit number the tens digit is three times the units digit. The number is 54 more than the sum of its digits. Find the number.

Let the tens digit be $x$ and the units digit $y.x=3y$, and $(10x+y)-(x+y)=54$ gives $9x=54$, so $x=6$ and $y=2$. The number is 62. Check: $6=3\times 2$, and 62 - 8 = 54. 93 satisfies only the first condition $(9=3\times 3)$ but 93 - 12 = 81, not 54; 39 has the digit relation the wrong way round; 26 is the answer with its digits swapped.