Solutions Change in Profit Sharing Ratio TS Grewal Class 12 [2025-26]
Table of Contents
Sacrificing and Gaining Share
Question Nos 1 to 4
Question 1:
Om and Shyam are sharing profits and losses equally. With effect from 1st April 2023, they agree to share profits in the ratio of 4 : 3. Calculate the individual partner’s gain or sacrifice due to the change in ratio.
Solution
Old Ratio = 1 : 1
New Ratio = 4 : 3
Om’s share = \(\frac{1}{2}\) – \(\frac{4}{7}\) = \(\frac{7 – 8}{14}\) = \(\frac{-1}{14}\) (gain)
Shyma’s share = \(\frac{1}{2}\) – \(\frac{3}{7}\) = \(\frac{7 – 6}{14}\) = \(\frac{1}{14}\) (sacrifice)
Question 2:
Ahilya, Laxmi and Parvati are sharing profits and losses in the ratio of 5 : 3 : 2. With effect from 1st April, 2024, they decide to share profits and losses in the ratio of 5 : 2 : 3. Calculate each partner’s gain or sacrifice due to change in ratio.
Solution
Old Ratio = 5 : 3 : 2
New Ratio = 5 : 2 : 3
Ahilya’s share = \(\frac{5}{10}\) – \(\frac{5}{10}\) = \(\frac{5 – 5}{10}\) = 0 (No sacrifice / No gain)
Laxmi’s share = \(\frac{3}{10}\) – \(\frac{2}{10}\) = \(\frac{3 – 2}{10}\) = \(\frac{1}{10}\) (sacrifice)
Parvati’s share = \(\frac{2}{10}\) – \(\frac{3}{10}\) = \(\frac{2 – 3}{10}\) = \(\frac{-1}{10}\) (gain)
Question 3:
X, Y, and Z are sharing profits and losses in the ratio of 5 : 3 : 2. With effect from 1st April 2023, they decide to share profits and losses equally. Calculate each partner’s gain or sacrifice due to the change in the ratio.
Solution
Old Ratio = 5 : 3 : 2
New Ratio = 1 : 1 : 1
X’s share = \(\frac{5}{10}\) – \(\frac{1}{3}\) = \(\frac{15 – 10}{30}\) = \(\frac{5}{30}\) (sacrifice)
Y’s share = \(\frac{3}{10}\) – \(\frac{1}{3}\) = \(\frac{9 – 10}{30}\) = \(\frac{-1}{30}\) (gain)
Z’s share = \(\frac{2}{10}\) – \(\frac{1}{3}\) = \(\frac{6 – 10}{30}\) = \(\frac{-4}{30}\) (gain)
Question 4:
A, B, and C are partners sharing profits and losses in the ratio of 5 : 4 : 1. Calculate the new profit sharing ratio, sacrificing ratio, and gaining ratio in each of the following cases:
Case 1. As per new agreement, C acquires 1/5th share from A.
Case 2. As per new agreement, C acquires 1/5th share equally from A and B.
Case 3. As per new agreement, A, B, and C will share future profits and losses equally.
Case 4. As per new agreement, C acquires 1/10th share of A and 1/2 share of B.
Solution
Case 1
Old Ratio = 5 : 4 : 1
C acquires 1/5th share from A.
A’s new share = \(\frac{5}{10}\) – \(\frac{1}{5}\) = \(\frac{5 – 2}{10}\) = \(\frac{3}{10}\)
B’s new share = \(\frac{4}{10}\) – 0 = \(\frac{4}{10}\)
C’s new share = \(\frac{1}{10}\) + \(\frac{1}{5}\) = \(\frac{1 + 2}{10}\) = \(\frac{3}{10}\)
New Profit sharing ratio = \(\frac{3}{10}\) : \(\frac{4}{10}\) : \(\frac{3}{10}\) = 3 : 4 : 3
Case 2
Old Ratio = 5 : 4 : 1
C acquires 1/5th share equally from A and B.
C acquires from A = \(\frac{1}{5}\) \(\times\) \(\frac{1}{2}\) = \(\frac{1}{10}\)
C acquires from B = \(\frac{1}{5}\) \(\times\) \(\frac{1}{2}\) = \(\frac{1}{10}\)
A’s new share = \(\frac{5}{10}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\)
B’s new share = \(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)
C’s new share = \(\frac{1}{10}\) + \(\frac{1}{5}\) = \(\frac{3}{10}\)
New Profit-sharing ration = \(\frac{4}{10}\) : \(\frac{3}{10}\) : \(\frac{3}{10}\) = 4 : 3 : 3
Sacrificing Ration of A & B = \(\frac{1}{10}\) : \(\frac{1}{10}\) = 1 : 1
Case 3
