Question

Rani, Maharani and Laxmi were partners in a firm sharing profits and losses in the ratio of 3 : 3 : 2. On 1stApril, 2024 they admitted Reena as a new partner for \( \frac{1}{5} \) share in the profits of the firm. Reena acquired her share from Rani and Maharani in the ratio of 3 : 2. The new profit sharing ratio between Rani, Maharani, Laxmi and Reena will be :

• A. 51 : 59 : 40 : 50
• B. 51 : 59 : 50 : 40
• C. 59 : 51 : 50 : 40
• D. 40 : 51 : 59 : 50

Hint:

Always adjust old partners’ shares for the sacrificed portion when a new partner is admitted. Calculate the new ratio precisely in fractions before converting to whole numbers.

Answer 1

The Correct Option is B

Old ratio of Rani, Maharani, Laxmi = 3 : 3 : 2.
Reena is admitted for a \( \frac{1}{5} \) share in profits. The remaining share for the old partners is \( 1 - \frac{1}{5} = \frac{4}{5} \).
Reena acquires her \( \frac{1}{5} \) share from Rani and Maharani in the ratio 3 : 2.
Calculations:
Rani's sacrifice = \( \frac{3}{5} \times \frac{1}{5} = \frac{3}{25} \).
Maharani's sacrifice = \( \frac{2}{5} \times \frac{1}{5} = \frac{2}{25} \).
Laxmi does not sacrifice any share.
Old shares:
Rani = \( \frac{3}{8} \).
Maharani = \( \frac{3}{8} \).
Laxmi = \( \frac{2}{8} = \frac{1}{4} \).
New shares of Rani and Maharani:
Rani = \( \frac{3}{8} - \frac{3}{25} = \frac{75 - 24}{200} = \frac{51}{200} \).
Maharani = \( \frac{3}{8} - \frac{2}{25} = \frac{75 - 16}{200} = \frac{59}{200} \).
Laxmi's share = \( \frac{1}{4} \times \frac{4}{5} = \frac{1}{5} = \frac{40}{200} \).
Reena's share = \( \frac{1}{5} = \frac{40}{200} \).
New ratio = 51 : 59 : 40 : 40.
The correct answer is (B).