A, B and C are partners sharing profits in the ratio of 3 : 2 : 1. A retires and his share is taken up by B and C in the ratio of 3 : 2. Calculate the new profit sharing ratio.

19:11

The correct answer is Option (2) → 19:11

Old Ratio of A, B, and C $=3:2:1$

A's share (Retiring Partner) $=3/6$

A's share is taken up by B and C in the ratio 3:2.

B's Gain: He takes 3/5​ of A's share.​

B’s Gain=3/6 * 3/5 = 9/30

C's Gain: He takes 2/5 of A's share.

C’s Gain=3/6 * 2/5 = 6/30

New Share=Old Share+Gain

B’s New Share=2/6 + 9/30 = 19/30

C’s New Share= 1/6+ 6/30 = 11/30

New Ratio of B and C= 19:11