Question

A and B are partners in a firm sharing profits and losses in the ratio of 5:3 . They admit C and D as new partners. A sacrifices 1/2 of his share in favour of C and B sacrifices 1/4 from his share in favour of D . Calculate their new profit sharing ratio . (Ans. New ratio 5:2:5:4)​

Answer 1

Given:

• A and B are partners in a firm, sharing profits and losses in the ratio 5:3.
• C and D are admitted as new partners.
• A sacrifices 1/2 of his share for C and B sacrifices 1/4 of his share for D.

To find: The new ratio.

Answer:

• A's old share = 5/8
• B's old share = 3/8

From A, C gets:

• 1/2 × 5/8 = 5/16

Reduction in B's share = B's share - Sacrifice for D:

• 3/8 - 1/4 = (3 - 2)/8 = 1/8

Calculation of the new ratio:

New ratio = Old ratio - Sacrifice made

For A:

• New ratio = 5/8 - 5/16 = (10 - 5)/16 = 5/16

For B:

• New ratio = 3/8 - 1/4 = 1/8, or 2/16

For C:

• New ratio = 5/16

For D:

• New ratio = 1/4, or 4/16

Therefore, the new profit-sharing ratio is 5:2:5:4.

• When the question specifies 'of', you need to multiply them.
• When the question specifies 'from', you need to subtract from the old shares.