According to the question,

A completes the work in 5×2=10 days

B completes the work in $10\times \frac{5}{2}=25$days

In 1 day,

A can complete $\frac{1 }{10}$^th of the work

B can complete $\frac{1}{25}$^th of the work

(A+B) together can complete $\frac{1}{10}+\frac{1}{25}=\frac{5+2}{50}=\frac{7}{50}$^th of the work

∴ (A+B) will complete the whole work in $\frac{50}{7}$ days.

∴ Required time =$\frac{50}{7}$=$7\frac{1}{7}$days.

 Hence option B is the correct.