​ A and B are partners sharing profits and losses equally (1:1). They admit C for 1/6 share in future profits. ​

Question

A and B are partners sharing profits and losses equally (1:1). They admit C for \(\frac{1}{6}\) share in future profits. Calculate the new ratio and sacrificing ratio.

Answer 1

Old Ratio = 1:1 C’s 

Share = 1/6 

Remaining portion = 1 – 1/6 = 5/6 

This 5/6 is to share among A & B in their old ratio.

So their new shares will be 

A’s share \(\frac{1}{2}\) of \(\frac{5}{6}\) = \(\frac{1}{2}\) × \(\frac{5}{6}\) = \(\frac{5}{12}\) 

B’s share  \(\frac{1}{2}\) of \(\frac{5}{6}\) =  \(\frac{1}{2}\) × \(\frac{5}{6}\) = \(\frac{5}{12}\) The new ratio between

A,B and C = \(\frac{5}{12}\) : \(\frac{5}{12}\) : \(\frac{2}{12}\)

Sacrificing ratio = Old ratio - New ratio

A's Sacrifice = \(\frac{1}{2} -\frac{5}{12} = \frac{6-5}{12} = \frac{1}{12}\)

B's Sacrifice = \( \frac{1}{2}- \frac{5}{6} = \frac{6-5}{12} = \frac{1}{12}\)

Sacrificing ratio = \(\frac{1}{12} : \frac{1}{12}\) = 1 : 1

Old ratio and sacrificing ratio are the same here.