Question

A and B are sharing profit and losses in the ratio 4:3. They agreed to share profits in the

ratio 3:2 in the future. Which statement is correct in this regard?

(a) A and B sacrificed 1/35th of their share of profit.

(b) A gained 1/35th share and B sacrificed 1/35th share of profit

(c) A gained 2/35th share and B sacrificed 2/35th share of profit.

(d) A sacrificed 1/35th share and B gained 1/35th share of profit.​

Answer 1

ANSWER :

❖ (b) A gained $\sf{\dfrac{1}{35}}$ th share and B sacrificed $\sf{\dfrac{1}{35}}$ th share of profit.

• ➺ If A and B are sharing profit and losses in the ratio 4 : 3 and they agreed to share profits in the ratio 3 : 2 in the future; then A will gain $\sf{\dfrac{1}{35}}$ th share and B will sacrifice $\sf{\dfrac{1}{35}}$ th share of profit.

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EXPLANATION :

❒ Given :-

• Old Profit Sharing Ratio of A and B = 4 : 3

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

❒ To Calculate :-

• Gain or Sacrifice of A and B = ?

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❒ Required Formula :-

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

❒ Note :-

• While calculating Sacrificing Ratio, if the sacrifice of a partner is negative, it implies the gain of the partner.

• While calculating Sacrificing Ratio, if the sacrifice of a partner js positive, it implies the sacrifice of the partner.

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❒ Calculation :-

It is given that,

• Old Profit Sharing Ratio of A and B = 4 : 3

So,

• A's Old Share = $\sf{\dfrac{4}{7}}$

• B's Old Share = $\sf{\dfrac{3}{7}}$

Again,

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

So,

• A's New Share = $\sf{\dfrac{3}{5}}$

• B's New Share = $\sf{\dfrac{2}{5}}$

We know that,

• ★ Sacrifice = Old Share - New Share

Using this formula,

• ✠ Sacrifice of A = A's Old Share - A's New Share

⇒ Sacrifice of A = $\sf{\dfrac{4}{7}}$ - $\sf{\dfrac{3}{5}}$

⇒ Sacrifice of A = $\sf{\dfrac{20 - 21}{35}}$

⇒ Sacrifice of A = $\sf{\dfrac{- 1 }{35}}$

While calculating Sacrificing Ratio, ifthe sacrifice of a partner is negative, it implies the gain of the partner.

• ✪ Gain of A = $\sf{\dfrac{1}{35}}$ th share of Profit

And,

• ✠ Sacrifice of B = B's Old Share - B's New Share

⇒ Sacrifice of B = $\sf{\dfrac{3}{7}}$ - $\sf{\dfrac{2}{5}}$

⇒ Sacrifice of B = $\sf{\dfrac{15 - 14}{35}}$

⇒ Sacrifice of B = $\sf{\dfrac{1}{35}}$

While calculating Sacrificing Ratio, if the sacrifice of a partner is positive, it implies the sacrifice of the partner.

• ✪ Sacrifice of B = $\sf{\dfrac{1}{35}}$ th share of Profit

Hence,

• ❍ A gained $\sf{\dfrac{1}{35}}$ th share and B sacrificed $\sf{\dfrac{1}{35}}$ th share of profit.