A two-digit number has 3 in its unit's place, and the sum of its two digits is one seventh of the number itself. Find the number.

The number is 63.

let the number be 10t + 3.

digit sum t + 3 = (10t + 3)/7.

7(t + 3) = 10t + 3.

7t + 21 = 10t + 3, so 3t = 18, t = 6.

the number = 10 x 6 + 3 = 63.