P and Q are partners sharing profits in the ratio of 2 : 1. They admitted R into partnership giving him $\frac{1}{5}$^th share which he acquired from P and Q in 1 : 2 ratio. Calculate the new profit sharing ratio.

3 : 1 : 1

The correct answer is Option (3) - 3 : 1 : 1.

Old ratio = 2:1 (P & Q)
R admit with 1/5th share
Sacrificing ratio = 1:2

P sacrifice = 1/5 x 1/3
                = 1/15

Q sacrifice = 1/5 x 2/3
                = 2/15

New share of P = 2/3 - 1/15
                      = (10-1)15
                      = 9/15

New share of Q = 1/3 - 2/15
                       = (5 -2)/15
                      = 3/15

NEW RATIO = 9/15 : 3/15 :1/5
                 = 9/15 : 3/15 : 3/15
                 = 9 :3:3
                = 3:1:1