The correct answer is (b) ~6%.
Relative Market Share (RMS) is defined as a company's market share, devided by the market share of it's largest competitor, e.g
- for Player A, it is it's own market share, devided by the share of Player E,
- for Player E it is it's own share, devided by the share of Player A
Therefore, you can express the total share of A, E, B in terms of the market share of Player A (let's call that MS(A)):
45% = 1 x MS(A) + 0.75 x MS(A) + 0.55 x MS(A)
==> MS(A) = 19.6%
Now you need to add the total share of the new company
MS(New) = 0.1 x MS(A) + 0.2 x MS(A), because RetailCo and Player D have a RMS of 0.1 and 0.2 respectively.
MS(New) = 0.3 x 19.6% = 6%
Hope this helps