Positive predictive value answers a clinically practical question: given a positive test, how likely is real disease? It is therefore computed down the column of everyone the test labelled positive.
The positive column here contains two kinds of people: the genuinely diseased who tested positive (true positives, $TP = 90$) and the disease-free who were wrongly flagged (false positives, $FP = 50$). The denominator is every positive result, $TP + FP = 140$.
Applying the definition:
\[ PPV = \frac{TP}{TP+FP} = \frac{90}{140} \approx 0.643 \]
Expressed as a percentage this is about $64.3\%$. In words, roughly two-thirds of positive results are correct and one-third are false alarms. Note that PPV depends on disease prevalence, unlike sensitivity and specificity; in a low-prevalence population the same test would yield a lower PPV because false positives would dominate.
\[\boxed{PPV \approx 64.3\%}\]