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 \(\frac{1}{5}\) share in profits. So, remaining share for old partners = \(1 - \frac{1}{5} = \frac{4}{5}\).
Reena acquires her \(\frac{1}{5}\) share from Rani and Maharani in the ratio 3 : 2.
Let’s calculate the exact shares:
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 = \(\frac{1}{5} = \frac{40}{200}\)
Hence, new ratio = 51 : 59 : 40 : 40
Thus, the correct answer is (B).