Ts Grewal Volume 1 - 2019

Retirement/Death of a Partner

Question 1:

A, B and C were partners sharing profits in the ratio of 1/2, 2/5 and 1/10. Find the new ratio of the remaining partners if C retires.

Answer 1:

Old Ratio (A, B and C) =

or 5 : 4 : 1

As we can see, no information is given as to how A and B are acquiring C's profit share after his retirement, so the new profit sharing ratio between A and B is calculated just by crossing out the C’s share. That is, the new ratio becomes 5 : 4.

∴ New Profit Ratio (A and B) = 5 : 4

Question 2:

From the following particulars, calculate new profit-sharing ratio of the partners:
(a) Shiv, Mohan and Hari were partners in a firm sharing profits in the ratio of 5 : 5 : 4. Mohan retired and his share was divided equally between Shiv and Hari.
(b) P, Q and R were partners sharing profits in the ratio of 5 : 4 : 1. P retires from the firm.

Answer 2:

(a)

Old Ratio (Shiv, Mohan and Hari) = 5 : 5 : 4

Mohan’s Profit Share =

His share is divided between Shiv and Hari equally i.e. in the ratio of 1: 1

New Profit Share = Old Profit Share + Share taken from Mohan

∴ New Profit Ratio (Shiv and Hari) = 15 : 13

(b)

Old Ratio (P, Q and R) = 5 : 4 : 1

P’s Profit Share =

As we can see, no information is given as to how Q and R are acquiring P's profit share after his retirement, so the new profit sharing ratio between Q and R is calculated just by crossing out the P’s share. That is, the new ratio becomes 4 : 1

∴New Profit Ratio (Q and R) = 4 : 1

Question 3:

R, S and M are partners sharing profits in the ratio of 2/5, 2/5 and 1/5. M decides to retire from the business and his share is taken by R and S in the ratio of 1 : 2. Calculate the new profit-sharing ratio.

Answer 3:

Old Ratio (R, S and M) = 2 : 2 : 1

M retires from the firm.

His profit share =

\frac{1}{5}

M’s share taken by R and S in ratio of 1 : 2

S h a r e t a k e n b y R : \frac{1}{5} \times \frac{1}{3} = \frac{1}{15} S h a r e t a k e n b y S : \frac{1}{5} \times \frac{2}{3} = \frac{2}{15}

New Ratio = Old Ratio + Share acquired from M

R' s N e w S h a r e : \frac{2}{5} + \frac{1}{15} = \frac{6 + 1}{15} = \frac{7}{15} S' s N e w S h a r e : \frac{2}{5} + \frac{2}{15} = \frac{6 + 2}{15} = \frac{8}{15}

∴ New Profit Ratio (R and S) = 7 : 8

Question 4:

A, B and C were partners sharing profits in the ratio of 4 : 3 : 2. A retires, assuming B and C will share profits in the ratio of 2 : 1. Determine the gaining ratio.

Answer 4:

Old Ratio (A, B and C) = 4 : 3 : 2

New Ratio (B and C) = 2 : 1

Gaining Ratio

New Ratio − Old Ratio

∴Gaining Ratio = 3 : 1

Question 5:

X, Y and Z are partners sharing profits in the ratio of 1/2, 3/10, and 1/5. Calculate the gaining ratio of remaining partners when Y retires from the firm.

Answer 5:

Calculation of Gaining Ratio

\begin{matrix} X & : & Y & : & Z \\ Old Ratio & = & \frac{1}{2} & : & \frac{3}{10} & : & \frac{1}{5} \\ = & \frac{5 : 3 : 2}{10} \end{matrix}

New Ratio after Y's retirement = 5 : 2

Gaining Share = New Share – Old Share

X' s Gain = \frac{5}{7} - \frac{5}{10} = \frac{15}{70} Z' s Gain = \frac{2}{7} - \frac{2}{10} = \frac{6}{70}

Gaining Ratio = 15 : 6 or 5 : 2

Question 6:

(a) W, X, Y and Z are partners sharing profits and losses in the ratio of 1/3, 1/6, 1/3 and 1/6 respectively. Y retires and W, X and Z decide to share the profits and losses equally in future.
Calculate gaining ratio.
(b) A, B and C are partners sharing profits and losses in the ratio of 4 : 3 : 2. C retires from the business. A is acquiring 4/9 of C's share and balance is acquired by B. Calculate the new profit-sharing ratio and gaining ratio.