K, L, M and N are partners sharing profits in the ratio of 3 : 2 : 1 : 4. K retires and his share is acquired by L & M in the ratio of 3 : 2. Calculate new profit sharing ratio between L, M & N.

19 : 11 : 20

The correct answer is Option (3) - 19 : 11 : 20.

K, L, M and N = 3 : 2 : 1 : 4
K retires and his share is acquired by L & M in the ratio of 3 : 2.
K's share = 3/10
L gains = 3/10 x 3/5
           = 9/50

M gains = 3/10 x 2/5
            = 6/50

L's new share = 2/10 + 9/50
                    = (10+9)/50
                    = 19/50

M's share = 1/10 + 6/50
              = (5+6)/50
              = 11/50

N's share = 4/10

NEW RATIO = 19/50 : 11/50 : 4/10
                 = 19/50 : 11/50 : 20/50
                 = 19:11:20