A, B and C are partners sharing profit in the ratio of 20%, 40% and 40%, means their profit-loss ratio = 2 : 4 : 4 = 1 : 2 : 2.

Share of new partner D = \(\frac{1}{8}\) ;

B’s sacrifice = \(\frac{3}{5}\) ;

C’s sacrifice = \(\frac{2}{5}\).

Now, sacrifice of old partners = News partner’s share x Sacrificing ratio of old partners

B’s sacrifice = \(\frac{1}{8}\times\frac{3}{5}=\frac{3}{40}\)

C’s sacrifice = \(\frac{1}{8}\times\frac{2}{5}=\frac{2}{40}\)

Now, New share = old share – sacrifice

B’s new Share = \(\frac{2}{5}-\frac{3}{40}=\frac{16-3}{40}=\frac{13}{40}\);

C’s new Share = \(\frac{2}{5}−\frac{2}{40}=\frac{16−2}{40}=\frac{14}{40}\)

There is no change in the A’s share i.e = \(\frac{1}{5}\) ;

D’s share = \(\frac{1}{8}\)

∴ New profit and loss ratio of partners A, B, C and D = \(\frac{1}{5}:\frac{13}{40}:\frac{14}{40}:\frac{1}{8}\)= 8 : 13 : 14 : 5

D receives his share from B and C in the ratio of 3 : 2 and not receiving anything from A.

∴ Sacrificing ratio of partners B and C = 3 : 2.