#### Page No 6.55:

#### 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.

#### Answer:

__(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

#### Page No 6.56:

#### Question 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.

#### Answer:

Kumar's share=3/10acquired by Lakshya and Manoj in 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 (as given in the question)

#### Page No 6.56:

#### Question 8:

*A, B, *and *C* were
partners in a firm sharing profits in the ratio of 8 : 4 : 3. *B* retires
and his share is taken up equally by *A* and *C*. Find the
new profit-sharing ratio.

#### Answer:

Old Ratio (A, B and C) = 8 : 4 : 3

B retires from the firm.

His profit share = 4/15

*B’s* *share taken by A and C in ratio of 1: 1*

Share taken by A: 4/15×1/2=2/15

Share taken by C: 4/15×1/2=2/15

New Ratio = Old Ratio + Share acquired from B

A's New Share: 8/15+2/15=10/15=2/3

C's New Share: 3/15+2/15=5/15=1/3

∴ New
Profit Ratio (A and C) = 2: 1

#### Page No 6.56:

#### Question 9:

*A, B, *and *C* are
partners sharing profits in the ratio of 5: 3: 2. *C* retires and his
share is taken by *A*. Calculate new profit-sharing ratio of *A*
and *B*.

#### Answer:

Old Ratio (A, B and C) = 5: 3: 2

C retires from the firm.

His profit share = 210

*C’s* *share is taken by A in entirety*

New Ratio = Old Ratio + Share acquired from C

A's New Share: 5/10+2/10=7/10

B's New Share: 3/10+0=310

∴ New
Profit Ratio (A and B) = 7: 3

#### Page No 6.56:

#### Question 10:

*P, Q* and *R* are partners sharing
profits in the ratio of 7:5:3. *P* retires and it is decided that
profit-sharing ratio between *Q* and *R *will be same as existing
between *P* and *Q*. Calculate New profit-sharing ratio and
Gaining Ratio.

#### Answer:

Calculation of Gaining Ratio

P :Q :R=7:5:3(Old ratio)

Q :R=7:5 (New ratio, same as between P & Q)

Gaining Ratio = New Ratio - Old Ratio

Q's Gain=7/12−5/15=35−20/60=15/60

R's Gain=5/12−3/15=25−12/60=13/60

Q :R=15:13

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## Chapter-6: Retirement of a partner | 2021-2022

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