#### 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* dies.

#### Answer:

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

#### 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 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.

#### Answer:

__(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

#### Question 3:

*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.

#### Answer:

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

#### Question 4:

*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.

#### Answer:

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

#### Question 5:

(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.

#### 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

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