Explanation:

- P and Q initially share profits in the ratio of 9:7.

- R is admitted with a 9/20th share of the profits.

- R takes 1/5th from P's share and 1/4th from Q's share.

- To calculate the sacrificial ratio:

- P's share reduced by (1/5) *(9/20) = 9/100.

- Q's share reduced by (1/4) *(9/20) = 9/80.

- Convert fractions to a common denominator to compare:

- P's loss = 72/800.

- Q's loss = 90/800.

- Simplify the ratio of losses: 72:90, which further simplifies to 4:5.

Answer: Option 4 - 4 : 5