A and B together can complete a piece of work in 10 2/7days white B and C together can complete the same work in 13 1/3 days. B is 25% more efficient than C. In how many days will A and C together complete the same work ?

B is 25% more efficient than C

=> Ratio of time taken by B and C = 4 : 5

Let time taken by B and C respectively be 4x and 5x days

=> $$\frac{1}{4x} + \frac{1}{5x} = \frac{1}{\frac{40}{3}}$$

=> $$\frac{9}{20x} = \frac{3}{40}$$

=> $$\frac{3}{x} = \frac{1}{2}$$

=> $$x = 6$$

Thus, time taken by B = 24 days and time taken by C = 30 days

Let time taken by A be y days

=> $$\frac{1}{y} + \frac{1}{24} = \frac{7}{72}$$

=> $$\frac{1}{y} = \frac{7}{72} - \frac{1}{24} = \frac{1}{18}$$

=> $$y = 18$$

Thus, (A + C)'s 1 day's work = $$\frac{1}{18} + \frac{1}{30} = \frac{4}{45}$$

$$\therefore$$ Time taken by A & C together

= $$\frac{45}{4} = 11\frac{1}{4}$$ days