Question

X and Y are partners sharing profits and losses in the ratio of 5 : 3. On admission, Z
brings Rs.70,000 as cash and Rs.43,000 against Goodwill. New profit ratio between X,
Y and Z is 7:5:4. The sacrificing ratio of X and Y is!
​

Answer 1

Given :

Old Ratio Of Partners - 5 : 3

New Ratio Of Partners - 7 : 5 : 4

To Find :

Sacrificing Ratio

Formula To Find :

${\boxed{\large{\rm{Sacrificing \: \: Ratio \: = Old \: share \: - New \: Share }}}}$

Solution :

Sacrificing Ratio Of X :

$\sf\to \: Old \: Share \: of \: X= \frac{5}{8}$

$\sf\to \: New \: Share \: of \: X \: = \frac{7}{16}$

$\sf \to \: SR \: = \frac{5}{8} - \frac{7}{16}$

$\sf\to \: \frac{5 \times 2}{8 \times 2} - \frac{7}{16}$

$\sf\to \: \frac{10 }{16} - \frac{7}{16}$

$\sf\to \: \frac{3}{16}$

Sacrificing Ratio Of Y :

$\sf\to \: Old \: share \: of \: Y\: = \frac{3}{8}$

$\sf\to \: New \: Share \: of \: Y \: = \frac{5}{16}$

$\sf\to \: SR\: = \frac{3}{8} - \frac{5}{16}$

$\sf\to \: \frac{3 \times 2}{8 \times 2} - \frac{5}{16}$

$\sf\to \: \frac{6}{16} - \frac{5}{16}$

$\to \sf \frac{1}{16}$

$\bullet \sf \: \frac{3}{16}: \frac{1}{16} = 3 :1$

$\therefore \sf Sacrificing \: Ratio \: of \: Partners \: = 3: 1$

Answer 2

Given:

• X and Y are partners in a firm, sharing profits and losses in the ratio 5:3.
• Z is admitted as a partner, bringing Rs 70,000 as capital and Rs 43,000 as premium.
• The new profit-sharing ratio is 7:5:4.

To find: The sacrificing ratio.

Answer:

• X's old share = 5/8
• Y's old share = 3/8

• X's new share = 7/16
• Y's new share = 5/16
• Z's new share = 4/16

Calculation of the sacrificing ratio:

Sacrificing ratio = Old ratio - New ratio

For X:

• Sacrificing ratio = 5/8 - 7/16 = (10 - 7)/16 = 3/16

For Y:

• Sacrificing ratio = 3/8 - 5/16 = (6 - 5)/16 = 1/16

Therefore, the sacrificing ratio of X and Y is 3:1.

The premium for goodwill will be distributed among the old partners accordingly on the admission of a new partner.

The journal entry for the same would be:

Gaining partner(s)' capital A/c ... Dr

• To sacrificing partner(s)' capital A/c