Simple ratio prob

[papgust]

Please bear with me if my doubt sounds silly to you. Here is a simple question in ratios.

On Main Street, the ratio of the number of residential buildings to the number of commercial buildings is 2 to 3. If three of the residential buildings were to be converted to commercial buildings and no new buildings were introduced, the ratio would be 3 to 5. What is the total number of residential and commercial buildings on Main Street?
(A) 200
(B) 120
(C) 80
(D) 72
(E) 50


My approach:
Assumed res and com = 2x, 3x

Then i translated sentence 2 as,
(2x - 3) / (3x + 3) = 3/5

By solving,
x = 21

Total no. of res = 2*21 = 42
Total no. of com = 3*21 = 63
Therefore, 42+63 = 105.

But the OA is B. The OE assumes the ratio separately i.e. r/c = 2/3 and (r - 3) / (c + 3) = 3/5 ....(1).
From here, they calculate r as (2c)/3 and substitute t in (1) and solve for c. And finally get values of c and r.

My question is why the ratio is assumed as 2 different variables (c and r). Ratio always has a common number (say x, as i have done in my approach). Why is my approach wrong?

Source: GMAT Hacks

[trindadesn]

I believe you made a calc error.

I'm not sure how you got x = 21

your approach is right -

(2x-3) / (3x+3) = 3/5
=> 5 (2x-3)= 3(3x+3)
=> 10x -15 = 9x +9
=>x = 24

therefore total bldgs = 24 * 5 = 120.

[papgust]

Oh yes! I didn't re-check my calculation. so stupid of me Thanks for pointing out