6810 bottles produced last month (of all three kinds)
1/3 of the 6810 were orange = 2270 are the oranges so 6810-2270 = 4540 (both limes and apples)
apples = 3 * limes
apples count is N
limes count is n
N=3n
N+n=4540
3n+n=4540
4n=4540
n=1135 (limes)
N= 3n = 3405 (apples)