Assume that for a certain product, brand a has 15%
market share, brand b has 20% market share, and brand c
has 65% market share. a new brand, brand d, enters the
market and captures 30% of the market. the total market
has not grown. if brands a, b, call lost share by the same
relative amount, then what percent of the market does
brand b have now?

Brand b has the 5% of the market.

Explanation:

The first market scenario has three brands that share the market as follow:

Initial market share

Brand a 15%

Brand b 20%

Brand c 65%

Then brand d captures 30% of the market as Brand a and Brand b lost the relative same amount of market share. Meaning they both lost the 15% of their market share.  

Brand d captures 30%

This capture leads to the following market share:

Final market share:

Brand a 0%

Brand b 5%

Brand c 65%

Brand d captures 30%

As the incursion of Brand d captured the total share of Brand a then, the Brand A has to left the market.  Besides, the Brand b end up with a share of 5% of the total market share.

it was the first amendment

i normally just use