Answer : Option A

Explanation :

ATQ,
A: B = 1: 2........... (i)
B: C = 3: 2...........(ii)
C: D = 1: 3.......... (iii)
Now,
Find A: B: C: D
Step 1, A: B: C: D
1: 2 (A: B value by equation i)

Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the left-hand side the same is done.

i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

Or, A: B: C: D
1: 2: 2: 2
3: 3: 2: 2 (B: C value by equation ii)
1: 1: 1: 3 (C: D value by equation iii)

Now, multiply vertically and get A: B: C: D.

So, A: B: C: D = (1*3*1): (2*3*1): (2*2*1): (2*2*3)
Or, A: B: C: D = 3: 6: 4: 12