Question - Profit sharing ratio

Let  new share of firm be 1

D's Share is 1/6 therefore remaining share of firm is

1 - 1/6 = 5/6

C's Share = 1/6 or 6/36

Remaining share 5/6 - 1/6 = 4/6 

A's share = 4/6 * 3/6= 12/36

B'share = 4/6 * 2/6 = 8/36

A:B:C:D = 12:8:6:6 or   6:4:3:3

I think the answer is slightly incorrect.

A's share will be 4/6 * 3/5 = 12/30

B's share will be 4/6 * 2/5 = 8/30

(C's share is 1/6 or 5/30; D's share is 1/6 or 5/30)

So, the final ans will be 12:8:5:5.

(In the ratio 6:4:3:3, C's and D's share is 3/16 (each), which is certainly not 1/6.

But, in 12:8:5:5, C's and D's share is 5/30 (each), or 1/6.)

Please let me know if my reasoning is correct.

Agree with Mr.Romil.

C & D take 33.33 % share together.

So the balance 66.666 % has to be shared amongst A & B in the old ratio of 3 : 2.

Thus new share is A-40 %

                              B-26.66%

                              C-16.67%

                              D-16.67%

Here is the calculation.

Partners               Old Ratio                       Workings                          New Ratio

    A                        3/6 *5/5                        - 1/6 *3/5                              12/30

    B                        2/6 *5/5                        - 1/6 *2/5                                8/30

    C                        1/6 *5/5                                -                                      5/30

    D                            -                               + 1/6 *5/5                                5/30

New Ratio = A : B : C : D =>  12 : 8 : 5 : 5

Those who are unable to solve it, kindly brush up their concepts.