#### Question 1:

*Gita, 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.

#### Answer:

Old Ratio (*Gita, Radha
*and *Garv*) =1/2 :2/5 : 1/10
or 5 : 4 : 1

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

∴ New Profit Ratio (*Gita
and Radha*) = 5 : 4

#### Question 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.

#### Answer:

__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

#### Question 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.

#### 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 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 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.

#### 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 5:

*Sarthak**,
Vansh* and *Mansi* were
partners sharing profits in the ratio of 4 : 3 : 2. *Sarthak* retires, assuming *Vansh*
and *Mansi* will share profits in the ratio of 2 :
1. Determine the gaining ratio.

#### Answer:

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

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