A and B are partners sharing profits and losses equally (1:1). They a

1.	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» 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.

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»

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.