Study the following information carefully and answer the question. I. Bag X contains a total of 30 balls, which are either red or green. The probabili...

Study the following information carefully and answer the question.

I. Bag X contains a total of 30 balls, which are either red or green. The probability of selecting one red ball and one green ball from the bag is given as $\frac{40}{87}$. The number of red balls in the bag is $A$.

II. A certain number $B$ of green balls are taken out, painted red, and then placed back into Bag X.

III. After this, the probability of selecting two green balls from Bag X is $\frac{7}{29}$.

IV. All balls from Bag X are then transferred to Bag Y. From Bag Y, $C$ green balls are removed, and $(C-5)$ red balls are added. The probability of selecting two red balls from Bag Y is $\frac{2}{5}$.

Question: Find the value of $C$.