A can do 20% of a work in 4 days, and B can do 33⅓% of the same work in 10 days. They worked together for 9 days and then C completed the remaining work in 6 days. B and C together will complete 75% of the same work in:

A can do 20% of the work in 4 days.

B can do $$33 \frac{1}{3}\%$$​ of the work in 10 days.

A and B worked together for 9 days.

C completed the remaining work in 6 days.

The work rate is  expressed as the fraction of the work completed per day.

Work done per day by A: $$\text{Work rate of A} = \frac{20\%}{4} = \frac{1}{20} \text{ of the work per day}$$​

Work done per day by B: \text{Work rate of B} = $$\frac{\frac{1}{3}}{10} = \frac{1}{30} \text{ of the work per day}$$​

​$$\text{Work rate of A and B together} = \frac{1}{20} + \frac{1}{30} \\\text{Work rate of A and B together} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12} \\\text{Work done in 9 days} = 9 \times \frac{1}{12} = \frac{9}{12} = \frac{3}{4} = 75\%$$ 

​So, A and B together completed 75% of the work in 9 days.

C completed the remaining 25% of the work in 6 days.

​$$\text{Work rate of C} = \frac{25\%}{6} = \frac{1}{24} \text{ of the work per day}\\\text{Work rate of B and C together} = \frac{1}{30} + \frac{1}{24}\\\text{Work rate of B and C together} = \frac{4}{120} + \frac{5}{120} = \frac{9}{120} = \frac{3}{40} \text{ of the work per day}$$​​

Time required to complete 75% of the work:

​$$\text{Time required} = \frac{75\%}{\frac{3}{40}} = \frac{75}{100} \times \frac{40}{3} = \frac{3}{4} \times \frac{40}{3} = 10 \text{ days}$$