Question

X and Y are partners in a firm sharing profits and losses in proportion of 2:1. They admit a new partner Z for 1/6 share in profit. What is the new profit sharing ratio of X, Y and Z?

Answer 1

Explanation:

given,

old ratio= 2:1

z's share = 1/6

let the whole share be 1

remaining share be 1-1/6= 5/6

x new share - 5/6×2/3=10/18

y new share -5/6×1/3=5/18

z new share - 1/6×1/3= 1/18

new profit and loss sharing ratio is 10:5:1 .

Answer 2

Appropriate Question:

X and Y were partners in a firm sharing profit and losses in the ratio of 2:1. Z is admitted in the firm as a partner with 1/6th share which he acquires equally from X and Y. Calculate new profit sharing ratio of X, Y and Z

Solution:

We have old profit sharing ratio of X and Y.  

• X's share = 2/3
• Y's share = 1/3

Let's assume the total profit be 1.  

Z is admitted as a new partner with 1/6th share which he acquires equally from X and Y i.e. sacrifice ratio of both X and Y is 1/2.

• Z acquires share from X = 1/2 x 1/6 = 1/12
• Z acquires from Y = 1/2 x 1/6 = 1/12

New profit sharing ratio  

• X's new share = 2/3 - 1/12 = 7/12
• Y's new share = 1/3 - 1/12 = 3/12

Required profit sharing ratio is:  

⇒ X : Y : Z  

⇒ 1/6 : 7/12 : 3/12  

⇒ 2/12 : 7/12 : 3/12  

⇒ 2 : 7 : 3  

So the required ratio is 2:7:3.