A, B and C are partners sharing profits in the ratio of 3:2:1. They admit D for 1/6 share. C would retain his old share. What will be the new ratio of all partners?

12:8:5:5

The correct answer is option 3- 12:8:5:5.

D's share = 1/6
C will retain his old share. So, Only A and B sacrifice in ratio of 3 : 2

Calculation of sacrifice share :
A’s sacrifice = 3/5 of 1/6
                  = 3/30

B’s sacrifice = 2/5 of 1/6
                  = 2/30

C’s sacrifice = Nil

Calculation of New profit sharing Ratio :
New share = Old share – Sacrifice share

A’s new share = 3/6 – 3/30
                       = (15-3)/30
                       = 12/30

B’s new share = 2/6 – 2/30
                       = (10-2)/30
                       = 8/30

C’s new share = Same as old share i.e. 1/6

D’s new share = 3/30 + 2/30
                        = 5/30

New ratio among A, B, C and D
12/30 : 8/30 : 1/6 : 5/30
12/30 : 8/30 : 5/30 : 5/30
= 12 : 8 : 5 : 5