Question

X, Y and Z are partners in the ratio of 3 : 2 : 1. X retires and his share is taken up by Y and Z in the ratio of 3 : 2. Calculate new profit sharing ratio.

Hint:

New Ratio = Old Share + Acquired Share from retiring partner.

Answer 1

The old ratio of X, Y and Z is 3 : 2 : 1. Total share is 6 parts. X's share is 3/6. Y and Z take this share in the ratio of 3 : 2. Therefore, Y gets 3/5 of X's share which equals 3/6 × 3/5 = 9/30. Z gets 2/5 of X's share which equals 3/6 × 2/5 = 6/30. Their old shares were Y = 2/6 and Z = 1/6. Adding the gained shares, Y becomes 2/6 + 9/30 and Z becomes 1/6 + 6/30. After converting to a common denominator and simplifying, the new ratio of Y and Z becomes 19 : 11. This ratio represents how they will share profits after X's retirement.