TS Grewal chapter 6 – Retirement of a Partner, Question 1 to Question 7 solution of the 2021-22 Edition.
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Q.1- Geeta, Radha and Garv were partners sharing profits in the ratio of 1/2, 2/5 and 1/10. Find the new ratio of the remaining partners if Garv retires.
Solution:
Old Ratio (Geeta, Radha and Garv) =1/2 :2/5 : 1/10 or 5 : 4 : 1
As we can see no information is given as to how Geeta and Radha are acquiring Garv’s profit share after his retirement, so the new profit sharing ratio between Geeta and Radha is calculated just by crossing out the Garv’s share. That is, the new ratio becomes 5 : 4.
∴ New Profit Ratio (Geeta and Radha) = 5 : 4
Q.2- 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.
Solution:
Calculation of Gaining Ratio
X: Y: Z Old Ratio=1/2 : 3/10 : 1/5 = 5:3:2/10
New Ratio after Y’s retirement = 5 : 2
Gaining Share = New Share – Old Share
X’s Gain= 5/7 – 5/10 = 15/70
Z’s Gain= 2/7 – 2/10 = 6/70
Gaining Ratio = 15: 6 or 5: 2
Q.3- 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.
Solution:
(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 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
Q.4- 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.
Solution:
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 = 2/15
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
Q.5- Sarthak, Vansh and Mansi were partners sharing profits in the ratio of 4 : 3 : 2. Sarthak retires. Vansh and Mansi will share profits in the ratio of 2 : 1. Determine the gaining ratio.
Solution:
Old Ratio (Sarthak, Vansh and Mansi) = 4 : 3 : 2
New Ratio (Vansh and Mansi) = 2 : 1
Gaining Ratio = New Ratio − Old Ratio
Vansh’s gain = 2/3 – 3/9 = 6-3/9 = 3/9
Mansi’s gain=1/3 – 2/9 = 3-2/9 = 1/9
∴Gaining Ratio = 3: 1
Q.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.
Solution :
(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
Q.7- Kumar, Lakshya, Manoj and Naresh are partners sharing profits in the ratio of 3 : 2 : 1 : 4. Kumar retires and his share is acquired by Lakshya and Manoj in the ratio of 3 : 2. Calculate new profit-sharing ratio and gaining ratio of the remaining partners.
Solution :
Kumar’s share = 3/10 acquired by Lakshya and Manoj in ratio 3:2
Share acquired by Lakshya = 3/10 × 3/5 = 9/50
Share acquired by Manoj = 3/10 × 2/5 = 6/50
Lakshya’s New Share = 2/10 + 9/50 = 19/50
Manoj’s New Share = 1/10 + 6/50 = 11/50
Naresh’s share (as retained) = 4/10 or 20/50
New Profit Sharing Ratio = 19:11:20
Gaining Ratio = 3:2