Question

P, Q and R were partners in a firm sharing profits and losses in the ratio of 3 : 5 : 2. S was admitted as a new partner for \(\frac{1}{5}\) share in the profits of the firm. S acquired his share entirely from Q. The new profit sharing ratio among P, Q, R and S will be:

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

Hint:

When a new partner is admitted and acquires their share from an existing partner, only that partner's share changes — others remain the same.

Answer 1

The Correct Option is B

Step 1: Old Ratio of P : Q : R = 3 : 5 : 2
Step 2: Total Share = 3 + 5 + 2 = 10 parts
Q's original share = \(\frac{5}{10} = \frac{1}{2}\)
Step 3: S is admitted for \(\frac{1}{5}\) share, which he acquires entirely from Q.
Q gives \(\frac{1}{5}\) of the firm’s profit from his share.
New share of Q = Old share – Share given to S = \(\frac{1}{2} - \frac{1}{5} = \frac{5 - 2}{10} = \frac{3}{10}\)
S’s new share = \(\frac{1}{5} = \frac{2}{10}\)
P and R's shares remain unchanged:
P = \(\frac{3}{10}\), R = \(\frac{2}{10}\)
Now, the new shares are: P = \(\frac{3}{10}\), Q = \(\frac{3}{10}\), R = \(\frac{2}{10}\), S = \(\frac{2}{10}\)
Step 4: Multiply all by 10 to remove denominators: 3 : 3 : 2 : 2