What is the ratio of the total number of men to the total number of women working in all the departments together ?

Number of Men in HR= $$\ \frac{\ 1}{2}\times11\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 11}{100}\times\ 4600=253\ $$

Number of Men in Accounts=$$\ \frac{\ 3}{4}\times8\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 8}{100}\times\ 4600=276\ $$

Number of Men in Production= $$\ \frac{\ 3}{5}\times15\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 15}{100}\times\ 4600=414\ $$

Number of Men in IT= $$\ \frac{\ 1}{4}\times26\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 26}{100}\times\ 4600=299\ $$

Number of Men in Marketing= $$\ \frac{\ 1}{2}\times22\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 22}{100}\times\ 4600=506\ $$

Number of Men in Merchandising= $$\ \frac{\ 5}{6}\times18\%\ of\ 4600=\ \ \frac{\ 1}{2}\times\ \ \frac{\ 18}{100}\times\ 4600=690\ $$

Total men= 253+276+414+299+506+690=2438.

Total Women= 4600-2438=2162.

Ratio of men and women= $$\ \frac{\ 2438}{2162}=\ $$= $$\ \frac{\ 53}{47}\ $$

Hence, Option C