12th | Death  of a Partner | Question No.  1 To 5 | Ts Grewal Solution 2022-2023

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 dies.

 

Old Ratio (A, B and C) =1/2 :2/5 : 1/10 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 death, 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

 

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 died and his share was taken equally between Shiv and Hari.
(b) P, Q and R were partners sharing profits in the ratio of 5 : 4 : 1. P died from.

 

(a)

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

Mohan’s Profit Share = 5/14

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

Share of mohan taken by shiv=5/14×1/2=5/28

Share of mohan taken by Hari=5/14×1/2=5/28

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

Shiv’s new share=5/14+5/28=10+5/28=15/28           

Hari’s  new share=4/14+5/28=8+5/28=13/28

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

(b)

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

P’s Profit Share = 5/10

As we can see, no information is given as to how Q and R are acquiring P's profit share after his death, 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

 

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

 

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

M retires from the firm.

His profit share = 1/5

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

Share taken by R: 1/5×1/3=1/15

Share taken by S: 1/5×2/3=215

New Ratio = Old Ratio + Share acquired from M

R's New Share: 2/5+1/15=6+1/15=7/15

S's New Share: 2/5+2/15=6+2/15=8/15

∴ New Profit Ratio (R and S) = 7 : 8

 

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

 

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

New Ratio (B and C) = 2 : 1

Gaining Ratio=New Ratio − Old Ratio

B’s gain=2/3-3/9=6-3/9=3/9   

C’s gain=1/3-2/9=3-2/9=1/9   

∴Gaining Ratio = 3: 1

 

(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 died 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 died. A is acquiring 4/9 of C's share and balance is acquired by B. Calculate the new profit-sharing ratio and gaining ratio.

 

(a)

Old Ratio (W, X, Y and Z) = of 1/3;1/6: 1/3;1/6 or 2 : 1 : 2 : 1

New Ratio (W, X and Z) = 1 : 1 : 1

Gaining Ratio = New Ratio − Old Ratio

W's Gain=1/3-2/6=2-2/6=0/6

X's Gain=1/3-1/6=2-1/6=1/6

Z's Gain=1/3-1/6=2-1/6=1/6              

∴Gaining Ratio = 0: 1: 1

 

(b)

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

C’s Profit Share =2/9

A acquires 4/9 of C’s Share and remaining share is acquired by B.

Share acquired by A=2/9×4/9=8/81

Share acquired by B=C’s share- Share acquired by A=2/9-8/81=10/81

New Profit Share = Old Profit Share + Share acquired from C

A’s new share=4/9+8/81=36+8/81=44/81

B’s new share=3/9+10/81=27+10/81=37/81

New Profit Ratio A and B = 44: 37

Gaining Ratio = New Ratio − Old Ratio

A's Gain=44/81-4/9=44-36/81=8/81

B's Gain=37/81-3/9=37-27/81=10/81

∴Gaining Ratio = 8: 10 or 4: 5