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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.

Solution

✅ Correct Option: 2

Initial profit sharing ratio of A, B and C = 3 : 2 : 1

Total parts = 3 + 2 + 1 = 6

A's share = 36\frac{3}{6} = 12\frac{1}{2}

B's original share = 26\frac{2}{6} = 13\frac{1}{3}

C's original share = 16\frac{1}{6}


A retires and his share (12\frac{1}{2}) is taken up by B and C in the ratio 3 : 2.

B's gain from A's share = 35\frac{3}{5} × 12\frac{1}{2} = 310\frac{3}{10}

C's gain from A's share = 25\frac{2}{5} × 12\frac{1}{2} = 210\frac{2}{10} = 15\frac{1}{5}


New share of B = Original share + Gain from A's share

= 13\frac{1}{3} + 310\frac{3}{10}

= 10+930\frac{10 + 9}{30} = 1930\frac{19}{30}

New share of C = Original share + Gain from A's share

= 16\frac{1}{6} + 15\frac{1}{5}

= 5+630\frac{5 + 6}{30} = 1130\frac{11}{30}


New profit sharing ratio = B : C = 1930\frac{19}{30} : 1130\frac{11}{30} = 19 : 11

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