According to the original paper, R is the “ratio of the number of ‘true relationships’ to ‘no relationships’ among those tested in the field.” Since it is “ratio” and not “proportion”, if you have R=0.2 and have 200 true relationships, you will have 1000 (not 800) no relationships. So 50 correct null hypotheses are wrongly rejected for a total of 110 rejections, 60 of which are correct.

According to the original paper, R is the “ratio of the number of ‘true relationships’ to ‘no relationships’ among those tested in the field.” Since it is “ratio” and not “proportion”, if you have R=0.2 and have 200 true relationships, you will have 1000 (not 800) no relationships. So 50 correct null hypotheses are wrongly rejected for a total of 110 rejections, 60 of which are correct.

EDIT: I'll add to my answer to address your edit.

For the table you show, yes, PPV = 0.6. But, for this table, R=0.25 (200/800, the odds), not 0.2 (200/1000, the proportion of the total). Therefore, the computation using the Ioannidis formula is 0.30.25/(0.30.25+0.05) = 0.6, that is, the same value you get.