Page No 5.86:
Question 6:
X and Y are partners
in a firm sharing profits and losses in the ratio of 3 :
2. Z is admitted as partner with 1/4 share in profit. Z takes
his share from X and Y in the ratio of 2 :
1. Calculate new profitsharing ratio.
Answer:
Old
Profit Sharing Ratio amongst Partners (X and Y) is 3 : 2
Z is admitted for 1/4^{th} Share in Profits
Sacrificing Ratio of X and Y is 2 : 1
Z aquires =2/3×1/4=2/12 from X
Z aquires =1/3×1/4=1/12 from Y
New ratio= old ratio – new ratio
X‘s
new share=3/5 2/12 =3610/60=26/60
Y‘s
new share=2/5 1/12 =245/60=19/60
Z’s
share=1/4=15/60
New
ratio= 26:19:15
7
Page No 5.86:
Question 7:
Old ratio: S:J:B=1:1:1
T is admitted for 1/5 share
Let the total Profit of firm be 1
Remaining share of the SJB after T’s admission =
11/5=51/5=4/5
New share
S=4/5×1/3=4/15
S=4/5×1/3=4/15
S=4/5×1/3=4/15
T=1/5×3/3=3/15
New profit sharing ratio of all partners S:J:B:T = 4:4:4:3
Sacrificing ratio= Old – new
S=134/15=54/15=1/15
J=134/15=54/15=1/15
B=134/15=54/15=1/15
Sacrificing ratio of S:J:B=1:1:1
Page No 5.86:
Question 8:
Kabir and Farid are partners in a firm sharing profits and losses in the ratio of 7 : 3. Kabir surrenders 2/10th from his share and Farid surrenders 1/10th from his share in favour of Jyoti; the new partner. Calculate new profitsharing ratio and sacrificing ratio.
Answer:
Calculation of New Ratio
Old Ratio of Kabir and Farid
7 : 3
Kabir sacrifices his share of profit in favour of Jyoti=210
Farid sacrifices his share of profit in favour of Jyoti =110
Jyoti's Share=210+110=310
New Ratio = Old Share − Share Sacrificed
Kabir's New Share=710210=510Farid's New Share=310110=210
New Profit Sharing Ratio = 5 : 2 : 3
Calculation of Sacrificing Ratio
Since, Kabir and Farid are
sacrificing 2/10 share and 1/10 share respectively, therefore the sacrificing
ratio becomes 2 : 1.
Page No 5.86:
Question 9:
Find New Profitsharing Ratio:
(i) R and T are partners in a firm
sharing profits in the ratio of 3 : 2. S joins the firm. R surrenders
1/4th of his share and T 1/5th of his share in favour
of S.
(ii) A and B are partners. They admit C for 1/4th
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 1/5th share
in the profit. C acquires 1/5th of his share from A and 4/5th
share from B.
(iv) X, Y and Z are partners in the ratio of 3 : 2 : 1. W joins the firm as a new partner for
1/6th share in profits. Z would retain his original share.
(v) A and B are equal partners. They admit C and D
as partners with 1/5th and 1/6th share respectively.
(vi) A and B are partners sharing profits/losses in the
ratio of 3 : 2 . C is admitted for 1/4th
share. A and B decide to share equally in
future.
Answer:
_{(i)}

R 
T 
OLD RATION 
3 : 
2 : 
Sacrificing Ratio = Old Ratio × Surrender Ratio
R’s=3/5×1/4=3/20
T’s=2/5×1/5=2/25
New Ratio = Old Ratio − Sacrificing Ratio
R= 3/53/20=9/20
T=2/52/25=8/25
S’s Share = R’s Sacrifice + S’s Sacrifice
=3/20+2/25=23/100

R 

T 

S 
New profit sharing ratio = 
9/20 
: 
8/25 
: 
23/100 
= 
25/100 
: 
32/100 
: 
23/100 
= 
25 
: 
32 
: 
23 
(ii)

A 
B 
OLD RATION 
1 : 
1 
C admits for 1/4^{th} share of profit
Let the combined share of A, B and C be = 1
Combined share of A and B =1C’s share
=11/4=3/4
New Ratio = Combined share of A and B ×2/3
A’s=3/4×2/3=6/12
B’s=3/4×1/3=3/12

A 

B 

C 
New profit sharing ratio = 
6/12 
: 
3/12 
: 
¼ 
= 
6/12 
: 
3/12 
: 
3/12 
= 
2 
: 
1 
: 
1 
(iii)

A 
B 
OLD RATION 
3 : 
2 
C admits for 1/5share of profit
A’s sacrifice 
= C’s share× 1/5 

=1/5×1/5 

=1/25 
B’s sacrifice 
= C’s share× 4/5 

=1/5×4/5 

=4/25 
New Ratio = Old Ratio − Sacrificing Ratio
A’s =3/51/25=14/25
B’s=2/54/25=6/25

A 

B 

C 
New profit sharing ratio = 
14/25 
: 
6/25 
: 
1/5 
= 
14/25 
: 
6/25 
: 
5/25 
= 
14 
: 
6 
: 
5 
(iv)

X 
Y 
Z 
OLD RATION 
3 : 
2 : 
1 
W admits for 1/6 share of profit
Let combined share of all partner after W’s admission be = 1
Combined share X and Y in the new firm =1 Z’s share W’s share
=11/61/6
=4/6
New Ratio = Old Ratio × Combined share of X and Y
A’s 
=3/5×4/6 






=12/30 





B’s 
=2/5×4/6 






=8/30 






X 

Y 

Z 

W 

New profit sharing ratio = 
12/30 
: 
8/30 
: 
1/6 
: 
1/6 

= 
12/30 
: 
8/30 
: 
5/30 
: 
5/30 

= 
12 
: 
8 
: 
5 
: 
5 

(v)

A 
B 
OLD RATION 
1 : 
1 
C admits for 1/5 share
D admits for 1/6 share
Let combined share of all partner after C and D’s admission be = 1
Combined share of profit of A and B after C and D’s admission =1 C’s share Z’s share
=11/51/6
=19/30
New Ratio = Old Ratio × Combined share of A and B
A’s 
=1/2×19/30 






=19/60 





B’s 
=1/2×19/30 






=19/60 






X 

Y 

Z 

W 

New profit sharing ratio = 
19/60 
: 
19/60 
: 
1/5 
: 
1/6 

= 
19/60 
: 
19/60 
: 
12/60 
: 
10/60 

= 
19 
: 
19 
: 
12 
: 
10 

(vi)

A 
B 
OLD RATION 
3 : 
2 
C admits for 1/5 share of profit
Let the combined share of all partners after C’s admission be = 1
Combined share of A and B after C’s admission =1 C’s share
=11/4
=3/4
New ratio of A and B each= Combined share of A and B×1/2
=3/4×1/2=3/8 each

X 

Y 

Z 
New profit sharing ratio = 
3/8 
: 
3/8 
: 
¼ 
= 
3/8 
: 
3/8 
: 
2/8 
= 
3 
: 
3 
: 
2 
Page No 5.87:
Question 10:
Rakesh and Suresh are sharing profits in the ratio of 4 : 3. Zaheer joins and the new ratio among Rakesh, Suresh and Zaheer is 7 : 4 : 3. Find out the sacrificing ratio.
Answer:

Rakesh 
Suresh 
Zaheer 
OLD RATION 
4
: 
3 

NEW RATIO 
7
: 
4
: 
3 
Sacrificing Ratio = Old Ratio − Sacrificing Ratio
Rakesh’s 
=4/77/14 



=1/14 


Suresh’s 
=3/74/14 



=2/14 



Rakesh 

Suresh 

Sacrificing sharing ratio = 
1/14 
: 
2/14 

= 
1 
: 
2 
