Question

& B are partners sharing Profit & Loss in ratio 5 : 4 , C is admitted for 1/5th share. A & B decided to share equally in future. Sacrificing ratio will be:

Answer 1

Given:

• A and B are partners in a firm, sharing profits and losses in the ratio 5:4.
• C is admitted into the firm for 1/5th shares.
• A and B decide to share their future profits and losses equally.

To find: The sacrificing ratio.

• A's old share = 5/9
• B's old share = 4/9

• A's new share = 1/2
• B's new share = 1/2

Let the profit be assumed as 1.

Remaining profit for A and B = 1 - 1/5 - 4/5

The remaining profit will be distributed among A and B in their new ratio.

Calculation of the new profit-sharing ratio:

For A:

• New ratio = 4/5 × 1/2 = 4/10

For B:

• New ratio = 4/5 × 1/2 = 4/10

For C:

• New ratio = 1/5, or 2/10

Therefore, the new profit-sharing ratio is 4:4:2 or 2:2:1.

Calculation of the sacrificing ratio:

Sacrificing ratio = Old ratio - New ratio

• If the difference is positive, it is a sacrifice.
• If the difference is negative, it is a gain.

For A:

• Sacrificing ratio = 5/9 - 2/5 = (25 - 18)/45 = 7/45

For B:

• Sacrificing ratio = 4/9 - 2/5 = (20 - 18)/45 = 2/45

Therefore, the sacrificing ratio is 7:2.

Answer 2

Answer:

The sacrificing ratio of A and B =  $\frac{7}{45}$ :  $\frac{2}{45}$ = 7:2

Explanation:

• The Profit & Loss in ratio of A and B = 5 : 4  
• So, A's share = $\frac{5}{9}$  and B's share = $\frac{4}{9}$

• Now, C is sharing $\frac{1}{5}$th .
• Hence, A and B is sharing 4/5th portion  

• So, Remaining share for A and B is (1 - $\frac{1}{5}$) = $\frac{5-1}{5}$ = $\frac{4}{5}$

• Now, A & B decided to share equally, so,

       A's new share = $\frac{1}{2}$of $\frac{4}{5}$ =$\frac{4}{10}$

       B's new share = $\frac{1}{2}$ of $\frac{4}{5}$  =$\frac{4}{10}$

• So, A's sacrifice = Old share - New share = $\frac{5}{9}$ -$\frac{4}{10}$ =$\frac{ (50 - 36)}{90}$  = $\frac{14}{90}$

        = $\frac{7}{45}$

• So, B's sacrifice = Old share - New share =  $\frac{4}{9}$  -$\frac{4}{10}$ = $\frac{40 - 36}{90}$  = $\frac{4}{90}$= $\frac{2}{45}$

        So, we can say that the sacrificing ratio of A and B =  $\frac{7}{45}$ :  $\frac{2}{45}$ = 7:2

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