Question

A, B, C and D were partners sharing profits in the ratio of 2 : 1 : 3 : 4. B retires and his share is acquired by A and C in the ratio of 4 : 1. Calculate the new ratio and the gaining ratio.

Answer 1

B's share will be divided between A and C in the ratio of 4 :1

A will gain $\frac{4}{5}of\frac{1}{10}=\frac{4}{50}$

Hence, A's new share $=\frac{2}{10}+\frac{4}{50}=\frac{10+4}{50}=\frac{14}{50}$

C will gain $\frac{1}{5}of\frac{1}{10}=\frac{1}{50}$

Hence, C's new share $=\frac{3}{10}+\frac{1}{50}=\frac{15+1}{50}=\frac{16}{50}$

D's share will remain the same i.e. $\frac{4}{10}$

New Ratio of A, C and $D=\frac{14}{50}:\frac{16}{50}:\frac{4}{10}or\frac{14:16:20}{50}or7:8:10.$

Gaining Ratio : Since A and C have acquired B's share in the ratio of 4 : 1, the gaining ratio will be 4 : 1 between A and C.