Question

A and B were partners in a firm sharing profits and losses in the ratio of 5:3. They admitted C as a new partner. The new profit sharing ratio between A, B and C was 3:2:3. A surrendered 1/5th of his share in favor of C. Calculate B's sacrificing ratio​

Answer 1

ANSWER :

• ❖ If A and B were partners in a firm sharing profits and losses in the ratio of 5 : 3 and after admitting C as a new partner, the new profit sharing ratio between A, B and C became 3 : 2 : 3 and A surrendered $\sf{\dfrac{1}{5}}$ th of his share in favor of C; then Sacrifice of B will be $\underline{\sf{\dfrac{1}{8}}}$

___________________________________________________________

SOLUTION :

❒ Given :-

• A and B were partners in a firm sharing profits and losses in the ratio of 5 : 3.

• C was admitted as a new partner and the new profit sharing ratio between A, B and C was 3 : 2 : 3.

❒ To Calculate :-

• Sacrifice of B = ?

❒ Understanding the Concept :-

• ✎ Sacrifice of a partner is the difference between what the partner was getting earlier and what he is getting now.

• ✎ In the question, the old profit sharing ratio and the new profit sharing ratio are given.

• ✎ In order to calculate the sacrifice of a partner, the new share of profit of the partner is to be deducted from the old share of profit of the partner.

____________________________________________

❒ Calculation :-

Here,

• Old Profit Sharing Ratio of A and B = 5 : 3

So,

• ✠ Old Share of Profit of B = $\sf{\dfrac{3}{8}}$

And,

• New Profit Sharing Ratio of A, B and C = 3 : 2 : 3

So,

• ✠ New Share of Profit of B = $\sf{\dfrac{2}{8}}$

We know that,

• $\dag \: \: \underline{ \boxed{ \bold{ \: Sacrifice = Old \: \: Share - New \: \: Share \: }}}$

Using this formula, we get,

• ✪ Sacrifice of B = Old Share of B - New Share of B

⇒ Sacrifice of B = $\sf{\dfrac{3}{8}}$ - $\sf{\dfrac{2}{8}}$

⇒ Sacrifice of B = $\sf{\dfrac{3 - 2}{8}}$

∴ Sacrifice of B = $\sf{\dfrac{1}{8}}$