Calculate the new profit-sharing ratio if A and B are partners in a firm sharing profits in ratio of 3:2, and C joins the firm and A surrenders 1/4th of his share and B surrenders 1/5th of his share in favour of C?

45:32:23

The correct answer is option 3- 45:32:23.

Old ratio = 3:2
A surrenders 1/4th of his share and B surrenders 1/5th of his share in favour of C.

Sacrifice of A = 1/4 x 3/5
                     = 3/20
Sacrifice of B = 1/5 x 2/5
                    = 2/25

So, C new share = 3/20 + 2/25
                           = (15+8)/100
                           = 23/100

A new share = 3/5-3/20
                     = (12-3)/20
                     = 9/20
B new share = 2/5-2/25
                     = (10-2)/25
                     = 8/25

So, new ratio = 9/20:8/25:23/100 or 45/100 : 32/100 : 23/100
                      = 45:32:23