Question

Porta 7. Sam and Pam share profits in the ratio of 2:1. Ram is admitted as a new partner and all the partners from then begin to share profits in the ratio 1:2:3. Find out the sacrificing ratio. [Ans. Sam sacrificed 3/6 th share]​

Answer 1

$\Large\mathtt\green{ }\huge\underline\mathtt\red{Answer : }$

R's old share= 5/8

S's old share= 3/8

T's share= R's sacrifice + S's sacrifice

               = [5/8 × 1/4] + [3/8 × 1/5]

               = [5/32] + [3/40]

               = 37/160

R's new share= 5/8- 5/32

                       = 15/32

S's new share= 3/8-3/40

                        = 12/40

New Profit sharing ratio= 75:48:37.

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Answer 2

Explanation:

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