A number of two digits has 3 for its unit's digit, and the sum of digits is 1/7 of the number itself, The number is

Let the ten's digit be x. Then, number = 10x + 3 and sum of digits = ( x + 3 )
So ,(x+3) = 1/7(10x + 3)
⇔ 7x + 21 = 10x + 3
⇔ 3x = 18
⇔ x=6
Hence, the number = 10x + 3 = (10 x 6) + 3 = 63.