Question

A, B and C were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. D was admitted as a new partner for $\dfrac{1}{5}$ share in the profits of the firm. D acquired his share entirely from A. The new profit sharing ratio between A, B, C and D will be:

• A. 5 : 2 : 2 : 1
• B. 3 : 3 : 2 : 2
• C. 3 : 2 : 3 : 2
• D. 4 : 3 : 2 : 1

Hint:

If a new partner acquires share from only one partner, reduce that partner’s share directly and adjust others only if mentioned.

Answer 1

The Correct Option is B

Old Ratio of A : B : C = 5 : 3 : 2
Total old share = 5 + 3 + 2 = 10
A’s original share = $\dfrac{5}{10} = \dfrac{1}{2}$
D is admitted for $\dfrac{1}{5}$ share, and it is taken entirely from A.
So, A’s new share = $\dfrac{1}{2} - \dfrac{1}{5} = \dfrac{5 - 2}{10} = \dfrac{3}{10}$
B’s share remains = $\dfrac{3}{10}$
C’s share remains = $\dfrac{2}{10}$
D’s share = $\dfrac{1}{5} = \dfrac{2}{10}$
Now, express all shares in a common denominator:
A : B : C : D = $\dfrac{3}{10} : \dfrac{3}{10} : \dfrac{2}{10} : \dfrac{2}{10}$
Multiplying each by 10 to eliminate denominators gives:
A : B : C : D = 3 : 3 : 2 : 2