JAMB 2004 · UME · Q2

Find $p$ if $451_6 - p_7 = 305_6$ .

Worked solution (try it first)

Change to base ten: $451_6 = 144 + 30 + 1 = 175$ and $305_6 = 108 + 5 = 113$ .
So $p = 175 - 113 = 62$ in base ten.
Write 62 in base seven: $62 = 1 \times 49 + 1 \times 7 + 6$ , so $p = 116_7$ , option C.