Multiple choice

A and B were equal partners in a firm. On $1-1-2001$, they admitted C on the following conditions: C should bring $Rs. 20,000$ as capital, and $Rs. 10,000$ as goodwill. In future A, B and C would share profits and losses in the ratio of $2 : 1 : 2$. A and B will share the goodwill in the ratio of _________.

  1. $1 : 1$
  2. $3 : 1$
  3. $1 : 3$
  4. $2 : 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Old ratio A:B = 1:1. New ratio A:B:C = 2:1:2. Sacrificing ratio = Old - New. A sacrifices 1/2 - 2/5 = 1/10. B sacrifices 1/2 - 1/5 = 3/10. Goodwill is shared in the ratio of sacrifice, which is 1/10 : 3/10 = 1:3.

AI explanation

The goodwill brought in by a new partner is distributed among the old partners according to the ratio of the profit share they surrender, calculated by subtracting their new profit share from their old profit share. A and B initially shared profits equally at 1 divided by 2 each, but in the new 2 to 1 to 2 ratio, A's share becomes 2 divided by 5 and B's share becomes 1 divided by 5. Therefore, A's sacrifice is 1 divided by 2 minus 2 divided by 5, which equals 1 divided by 10, while B's sacrifice is 1 divided by 2 minus 1 divided by 5, which equals 3 divided by 10. This gives a sacrificing ratio of 1 to 3 for A and B. The ratio is 1 to 3.

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