Goodwill for two-year purchase of average profit can be calculated using the formula given below:
$$Goodwill=\quad Average\quad profit\times No.\quad of\quad purchase\quad year$$
Substitute values in the above equation
$$Goodwill=\quad \frac { Rs39,000+Rs57,000+Rs24,000+Rs27,000-Rs12,000 }{ 5 } \times 2years\quad =\frac { Rs1,35,000 }{ 5 } \times 2\quad =Rs54,000$$
Now, sacrifising ratio of X, Y and Z has to be calculated using the formula given below
$$Sacrifising\quad ratio=\quad Old\quad ratio-New\quad ratio$$
X's sacrifising ratio$$=\quad \frac { 5 }{ 10 } -\frac { 2 }{ 10 } \quad =\frac { 3 }{ 10 } $$
Y's sacrifising ratio$$=\quad \frac { 3 }{ 10 } -\frac { 5 }{ 10 } \quad =\frac { -2 }{ 10 } $$
Z's sacrifising ratio$$=\quad \frac { 2 }{ 10 } -\frac { 3 }{ 10 } \quad =\frac { -1 }{ 10 } $$
As we see that Y and Z are gaining due to change in ratios but X has sacrifised
Y's gain$$=Rs54,000\times \frac { 2 }{ 10 } \quad =Rs10,800$$
Z's gain$$=Rs54,000\times \frac { 1 }{ 10 } \quad =Rs5,400$$
X's sacrifise$$=Rs54,000\times \frac { 3 }{ 10 } \quad =Rs16,200$$
Journal entry for adjustement
$$Gain\\ \quad To\quad Sacrifise$$
Substitute values in above equation
$$Y's\quad capital\quad a/c\quad Dr\quad Rs10,800\\ Z's\quad capital\quad a/c\quad Dr\quad Rs5,400\\ \quad \quad To\quad X's\quad capital\quad a/c\quad Rs16,200$$
Hence, Y is debited with $$Rs10,800$$ along with Z as $$Rs5,400$$ but X is credited with $$Rs16,200$$