a and b are partners sharing profits and losses in the ratio of 5:3. They admit C who will receive 1/4th share in future profits which he receives equally from A and B. Calculate new ratio and sacrificing ratio?
Answers
Explanation:
Solution :
★ Old Ratio :
A : B = 5 : 3
- A's Share = 5/8
- B's Share = 3/8
They admit C who will receive 1/4th share in future profits.
- C's Share = 1/4
Which he receives equally from A and B.
A's Sacrifice = 1/4 × 1/2 = 1/8
B's Sacrifice = 1/4 × 1/2 = 1/8
★ New profit sharing ratio :
• A's new share =
⇒ 5/8 - 1/8 = 4/8
• B's new share =
⇒ 3/8 - 1/8 = 2/8
• C's share =
⇒ 1/4 × 2/2 = 2/8
New profit sharing ratio =
- A : B : C
- 4/8 : 2/8 : 2/8
⇒ 4 : 2 : 2 = 2 : 1 : 1
New profit sharing ratio =
A : B : C = 2 : 1 : 1
★ Sacrificing ratio :
• A's Sacrifice = 1/8
• B's Sacrifice = 1/8
- A : B
- 1/8 : 1/8
⇒ 1 : 1
Therefore,
New profit sharing ratio =
A : B : C = 2 : 1 : 1 and Sacrificing ratio = A : B = 1 : 1
Given:-
a and b are partners sharing profits and losses in the ratio of 5:3.
C is admitted who received 1/4 th share in future profits
To Find:-
New ratio and sacrificing ratio
Solution:-
- As in the question profit and losses are shared in 5:3, it is the old ratio of a and b.
Finding out share of A:-
➺ Share of A = 5 / 5+3
➺ Share of A = 5 / 8
Finding out share of B:-
➺ Share of B = 3 / 5+3
➺ Share of B = 3 / 8
Finding out share of C:-
➺ Share of C = 1 / 2+2
➺ Share of C = 1/4
Finding out sacrifice of A:-
- Here we would multiply the share of C with 1/2 the result we would get would be same for both A and B
➺ Sacrifice of A and B = 1/4 × 1/2
➺ Sacrifice of A and B = 1×1 / 2×4
➺ Sacrifice of A and B = 1/8
Finding out new profit sharing ratio:-
- In order to calculate the new profit sharing ratio we would subtract share of both A and B with 1/8
A:-
➺ New profit sharing ratio of A = 5/8 - 1/8
➺ New profit sharing ratio of A = 5-1 / 8
➺ New profit sharing ratio of A = 4/8
B:-
➺ New profit sharing ratio of B = 3/8 - 1/8
➺ New profit sharing ratio of B = 3-1 / 8
➺ New profit sharing ratio of B = 2/8
C:-
- In order to calculate the new profit sharing ratio of C we would multiply the share of C with 2/2
➺ New profit sharing ratio of C = 1/4 × 2/2
➺ New profit sharing ratio of C = 1×2 / 4×2
➺ New profit sharing ratio of C = 2 / 8
Hence, new profit sharing ratio would be,
➺ New profit sharing ratio= 4/8 : 2/8 : 2/8
- Cancelling 8 in all of them,
➺ New profit sharing ratio = 4 : 2 : 2
- Cancelling by 2,
➺ New profit sharing ratio = 2 : 1 : 1
Hence,
- New profit sharing ratio is 2 : 1 : 1
Finding out sacrificing ratio:-
- In order to calculate the sacrifice ratio we would use the sacrifice of A and B. We have 1/8 as the sacrifice of both A and B.
=> Sacrificing ratio = 1/8 : 1/8
=> Sacrificing ratio = 8 / 8 : 1 / 1
=> Sacrificing ratio = 1 : 1
Hence,
- Sacrificing ratio of A : B is 1 : 1