Question

Find new Profit-Sharing Ratio:
(i) $R$ and $T$ are partners in a firm sharing profits in the ratio of $3:2$. $S$ joins the firm. $R$ surrenders $1/4^{th}$ of his share and $T$ surrenders $1/5^{th}$ of his share in favour of $S$.
(ii) $A$ and $B$ are partners.They admit $C$ for $1/4^{th}$ share. In future, the ratio between $A$ and $B$ would be $2:1$.
(iii) $A$ and $B$ are partners sharing profits and losses in the ratio of $3:2$. They admit $C$ for $1/5^{th}$ share in profit. $C$ acquires $1/5^{th}$ of his share from $A$ and $4/5^{th}$ share from $B$.
(iv) $X,Y$ and $Z$ are partners in the ratio of $3:2:1$. $W$ joins the firm as a new partners for $1/6^{th}$ share in profits. $Z$ would retain his original share.
(v) $A$ and $B$ are equal partners. they admit $C$ and $D$ as partners with $1/5^{th}$ and $1/6^{th}$ share respectively.
(vi) $A$ and $B$ are partners sharing profits/losses in the ratio of $3:2$. $C$ is admitted for $1/4^{th}$ share. $A$ and $B$ decide to share equally in future.

Answer 1

(i) R's old share= 3/5

T's old share= 2/5

R's sacrifice= 3/5 * 1/4

= 3/20

T's sacrifice= 2/5 * 1/5

= 2/25

New Profit Sharing ratio of the partners:

R= 3/5-3/20

= 9/20

T= 2/5-2/25

= 8/25

S= 3/20 + 2/25

= 23/100

Therefore,

Profit sharing ratio= 45:32:23

(ii) A's old share= 1/2

B's old share= 1/2

C is admitted for 1/4th share

Remaining share= 1-[1/4]

= 3/4

New Ratio between A and B should be 2:1

Hence, A's new share= 2/3 * 3/4

= 6/12

B's new share= 1/3 * 3/4

= 3/12

New Profit sharing ratio= 6:3:3

= 2:1:1

(iii) A's old share= 3/5

B's old share= 2/5

C is admitted for 1/5th share in the profit.

A's sacrifice= 1/5 * 1/5

= 1/25

B's sacrifice= 1/5 * 4/5

= 4/25

New profit sharing ratio of the partners:

A's new share= 3/5-1/25

= 14/25

B's new share= 2/5-4/25

= 6/25

C's share= 1/5

Ratio= 14:6:5

(iv) X's old share= 3/6

Y's old share= 2/6

Z's old share= 1/6

W is admitted for 1/6th share. Since, Z would retain his original share;

Remaining share= 1-[1/6]-[1/6]

= 4/6

X's new share= 4/6 * 3/5

= 12/30

Y's new share= 4/6 * 2/5

= 8/30

New Profit sharing ratio= 12:8:5:5

(v) A's old share= 1/2

B's old share= 1/2

C and D are admitted for 1/5th and 1/6th share respectively.

Hence, remaining share= 1- [1/5]- [1/6]

= 19/30

A's new share= 1/2 * 19/30

= 19/60

B's new share= 1/2 * 19/30

= 19/60

New Profit Sharing ratio= 19:19:12:10

(vi) A's old share= 3/5

B's old share= 2/5

C is admitted for 1/4th share.

Remaining share= 1-[1/4]

= 3/4

Since, A and B will share equally, their ratio is 1:1

A's new share= 1/2 * 3/4

= 3/8

B's new share= 1/2 * 3/4

= 3/8

New Profit sharing ratio= 3:3:2