Correct Answer - Option 1 : 12 : 8 : 5
Old Profit Sharing Ratio (X and Y) = 3:2
Z is admitted for a 1/5th share.
New Profit Sharing Ratio (X and Y) = 1 - 1/5 = 4:5
A's New Profit Sharing Ratio = 3/5 * 4/5 = 12/25
B's New Profit Sharing Ratio = 2/5 * 4/5 = 8/25
A: B: C = 12/25: 8/25: 1/5
Using the L.C.M method to make denominators common,
New Profit Sharing Ratio Of A:B: C is 12:8:5
Thus, option 1 is the correct answer.