Let right = $r$ Let total time = t

99% right, 50% of the total time: 99% $r$ $\times$ 50% $t$

= $\frac{99}{100}$ $r$ $\times$ $\frac{50}{100}$ $t$ = 0.495 $rt$

'Other.. time' implies (1 - 50%)t . Therefore,
99% wrong, the other 50% of the total time: (1 - 99%) $r$ $\times$ ( 1 - 50%) $t$

= $\frac{1}{100}$ $r$ $\times$ $\frac{50}{100}$ $t$ = 0.005 $rt$

Let $x$ % $rt$ be percentage of being right, all the time

percentage right, all the time = 99% right, 50% of the time + [1 - (99% wrong), the other % of the time)]

$x$ % $rt = 0.495rt + 0.005rt = 0.5rt$
$= 50$ % $rt$

Therefore $x = 50$