I’m sorry that it didn’t work for you this time round - but it’s a good opportunity to learn for next time.

So there is a really important second order question here: how is the growth distributed? There are a number of ways that it could be distributed:

- Primarily / entirely in one of the two sub-segments (probably sub-segment A)
- Proportionally across both segments

Assuming it impacts on both sub-segments; and that we expect year three to continue to have a similar growth and decline for the two sub-segments, I'd approach this by:

Calculate what the market share in year 3 would have been for the two sub-segments without any additional market growth:

- Sub-segment A would grow by 20% - and so would be 144 (120*1.2). Sub-segment B would be 81 (90*0.9).
- In total this gives you a market size of 225.
- Sub-segment B therefore has a market share of 36%. This is easily calculated by dividing 81 by 225. Divide both sides (top and bottom of the fraction) by 9 to give you 9 over 25. This is then a relatively simple division.
- Therefore sub-segment A has a market share of 1-36% = 64%

Apply these market shares to the overall market size of 231.

- Sub-segment A = 64% * 231 = roughly 148
- Sub-segment B = 231 - 148 = 83

If, however, the interviewer says that you don't expect to see a continued growth / decline then I'd use the market shares from year 2. And of course if the growth impacts primarily on one sub-segment then I'd use the calculations for year 3 without any growth for the sub-segment that isn't growing.

(edited)

Interesting analysis and clearly different from the approach I followed in the comment below. I am wondering though as to why would relative market share of A and B remain constant from year 2 to 3 if A is growing and B is expected to decline.

I'm saying exactly that - that they change. So first you need to calculate the what the values of A and B would be if the market changed from year 2 to 3 in the same way that it had from year 1 to 2: Year one: A = 100; B=100 Year two: A = 120 (growth of 20%); B=90 (decline of 10%) Then year three: A=120*1.2 = 144; B=90*0.9=81. A + B = 225 However, the market has grown overall. So if you assume that both segments are equally impacted by this overall market growth, then you need to know what proportion of the new market they would have. This is where you calculate A's market share as 64% (144/225) and B's as 36% (81/225). Then apply these percentages to the new total market of 231. So A's total value is 64%*231 = 148 and so on. Does that make sense?

"So if you assume that both segments are equally impacted by this overall market growth, then you need to know what proportion of the new market they would have" This is in contradiction to the initial condition that A is growing faster than the market and B is declining 10% -- I don't think it is necessary that both segments are equally impacted. However, that condition will a solution out of many different possible ones such as the one I have calculated below.

Your solution is accurate if the growth is all in segment A. But it might not be. To try to make this tangible: Let’s say that we’re talking about two burger stands in a football stadium. One sells vegan burgers (sub-segment A) and one sells meat burgers (sub-segment B). It’s a small stadium and in year 1 there are 200 seats. The proportion of people eating meat and vegan burgers is equal - so 100 get a meat burger and 100 get a vegan one. The next year they build a little extension and add 5% additional capacity - so 10 new seats, so the stadium can accommodate 210 people. The people who turn up are getting more environmentally conscious, so more opt for the vegan burger than the meat burger. Now 90 people go for the meat one (a 10% reduction) and 120 go for the vegan one (a 20% growth). If they hadn’t added the additional 10 seats then maybe 85 would have had meat (a 15% reduction) and 115 would have had vegan (a 15% growth), but they had the new people come in who pushed the figures up. But we don’t know what the switch would have been if we hadn’t had the capacity expansion. In year 3 they add another 10% capacity, or 21 seats. So the question is - are all these new people vegans or do some eat meat? This is why we need to know how the growth is split over the segments. If they’re all vegans (sub-segment A) then your calculation is accurate - we’ll see a reduction in 10% of meat eaters as people make the switch from meat to vegan, and all the growth will be in vegan burgers. However, what if some of them are meat eaters? Therefore the calculation I proposed assumed that the proportion of vegan to meat eaters in the new seats would mirror that of year 2. I hope that makes sense!

Thanks for explaining that. My point was actually the fact that there are multiple solutions possible depending on the conditions imposed (while what you state might be true in a veg/non veg scenario, there is really no reason to believe that it is true also for A and B). Therefore, there is no one accurate solution unless there is additional rationale , is what I am attempting to suggest.