12th | Admission of a partner | Question No. 11 To 15 | Ts Grewal Solution 2024-2025

Karim and Rehman are partners sharing profits in the ratio of 3 : 2. Naval is admitted as a partner. The new profit-sharing ratio among Karim, Rehman and Naval is 4 : 3 : 2. Find out the sacrificing ratio.

	Karim	Rehman	Naval
OLD RATION	3 :	2
NEW RATIO	4  :	3  :	2

Sacrificing Share = Old Ratio − New Ratio

Karim’s	=3/5-4/9
	=7/45
Rehman’s	=2/5-3/9
	=3/45
		Karim			Rehman
Sacrificing sharing ratio =		7/45		:	3/45
=		7		:	3

A, B and C are partners sharing profits in the ratio of 4 : 3 : 2. D is admitted for 1/3rd share in future profits. What is the sacrificing ratio?

	A		B		C
OLD RATIO  =	4	:	3	:	2

 

D is admitted for 1/3share of profit

Let the combined share of profit of A, B C and D be = 1

Combined share of A, B and C after D’s admission = 1 − D’s shares

=1-1/3

=2/3    

New Ratio = Old Ratio  combined share of A, B and C

A’s	=4/9×2/3
	=8/27
B’s	=3/9×2/3
	=6/27
C’s	=2/9×2/3
	=4/27

Sacrificing Ratio = Old Ratio − New Ratio                          

A’s	=4/9-8/27
	=4/27
B’s	=3/9-6/27
	=3/27
C’s	=2/7-4/27
	=2/27
		A			B			C
Sacrificing sharing ratio =		4/27		:	3/27		:	2/27
=		4		:	3		:	2

 

Gautam and Yashica are partners sharing profits and losses in the ratio of 3 : 2. They admit Asma into partnership. Gautam gives 1/3rd of his share while Yashica gives 1/10th from his share to Asma. Calculate new profit-sharing ratio and sacrificing ratio.

Old Ratio of Gautam and Yashica is 3 : 2.

Gautam 's sacrifice=1/3×3/5=3/15

Yashica 's sacrifice=1/10

Sacrificing Ratio=3/15:1/10 or  2 :1

New Ratio = Old Share − Share Sacrificed

Gautam 's new share=3/5-3/15=6/15

Yashica 's new share=2/5-1/10=3/10

Asma's share=3/15+1/10=9 30

New Ratio=6/15 : 3/10 : 9/30 = 4 :3 : 3

 

A, B and C are partners sharing profits in the ratio of 2 : 2 : 1. D is admitted as a new partner for 1/6th share. C will retain his original share. Calculate the new profit-sharing ratio and sacrificing ratio. 

Calculation of New Profit Sharing Ratio

Old Ratio of A, B and C  is 2 : 2 : 1

. D is admitted for 1/6th share while . C will retain his 1/5 original share

Remaining  share=1-1/6-1/5

=30-5-6/30=19/30

Remaining  share will be shared by A and B in 2:2  (old).

	A’s			=19/30×2/4
				=38/120
	B’s			=19/30×2/4
				=38/120
	C’s			=1/5×24/24
				=24/120
	D’s			=1/6×20/20
				=20/120
A			B			C		D
38		:	38		:	24	:	20
19		:	19		:	12	:	10

*Since nothing is mentioned about the sacrifice made by the existing partners, it is assumed that A and B sacrifice in their old ratio.

 

Calculation of Sacrificing Ratio

Sacrificing Ratio =Old ratio- new ratio

A’s	=2/5-19/60
	=24-19/60=5/60
B’s	=2/5-19/60
	=24-19/60=5/60

A : B = 5:5=1:1