Question

Sameer and Sohan were partners in a firm sharing profits and losses in the ratio of 4 : 3. On 1st April, 2024, they admitted Sudarshan as a new partner. The new profit sharing ratio on Sudarshan’s admission was 2 : 3 : 2. Sohan’s sacrifice on Sudarshan’s admission was:

• A. Nil
• B. $\dfrac{5}{21}$
• C. $\dfrac{4}{21}$
• D. $\dfrac{11}{21}$
  \textbf{Correct Answer:} (C) $\dfrac{4}{21}$

Hint:

To calculate a partner’s sacrifice: Sacrifice = Old Share – New Share. If both are equal, there is no sacrifice.

Answer 1

The Correct Option is C

Old ratio of Sameer and Sohan = 4 : 3
$\Rightarrow$ Total parts = 4 + 3 = 7
Sameer’s old share = $\dfrac{4}{7}$
Sohan’s old share = $\dfrac{3}{7}$

New profit sharing ratio among Sameer, Sohan, and Sudarshan = 2 : 3 : 2
$\Rightarrow$ Total parts = 2 + 3 + 2 = 7
Sameer’s new share = $\dfrac{2}{7}$
Sohan’s new share = $\dfrac{3}{7}$
Sudarshan’s new share = $\dfrac{2}{7}$

Now, compute the sacrifice = Old Share – New Share
Sohan’s old share = $\dfrac{3}{7} = \dfrac{9}{21}$
Sohan’s new share = $\dfrac{3}{7} = \dfrac{9}{21}$
$\Rightarrow$ Sohan’s sacrifice = $\dfrac{9}{21} - \dfrac{9}{21} = 0$

But since the question mentions a change to a new ratio 2 : 3 : 2, and if that was actually meant to be a sacrifice by both partners, we must calculate the sacrifice ratio:
Old Ratio = Sameer : Sohan = 4 : 3
New Ratio = Sameer : Sohan : Sudarshan = 2 : 3 : 2
Let’s convert both to 21 parts for easy comparison:
Old Ratio: Sameer = $\dfrac{4}{7} = \dfrac{12}{21}$, Sohan = $\dfrac{3}{7} = \dfrac{9}{21}$
New Ratio: Sameer = $\dfrac{2}{7} = \dfrac{6}{21}$, Sohan = $\dfrac{3}{7} = \dfrac{9}{21}$, Sudarshan = $\dfrac{2}{7} = \dfrac{6}{21}$

Sohan’s share remains unchanged, so no sacrifice.
$\Rightarrow$ Correct answer is (A) Nil, although if Sudarshan received some share from Sohan alone, a clarification in the question would be needed.