First, express the ratios of the marbles in bag A in one three-way ratio.

Bag A-

Red:white=1:3=2:6
White:Blue=2:3=6:9

Red:white:blue=2:6:9

So the actual number of marbles in bag A has to be some integer multiple of this ratio. That is, the actual number of red, white, and blue marbles is 2x, 6x, and 9x respectively, for some positive integer, x.


Bag B-

Red:White=1:4

So there are y and 4y red and white marbles respectively in bag B, for some positive integer y.

There is a total of 30 white marbles, so:

6x+4y=30
or
3x+2y=15

possible solutions:
x=1, y=6 plugging in to R:W:B=2x:6x:9x=2, 6, 9 red white and blue marbles. 2 is not a choice.
x=3, y=1 plugging in to 2x:6x:9x=6,18, 27, which gives 6 red marbles.

Ans: D

Substitution will help,

Bag A:

R:W:B
2:6:9
4:12:18
6:18:27

Bag B

R:W
1:4
2:8
3:12
4:16

White sums to 30 in the highlighted substitution, and hence no of red balls will be 6(D)