A man can do a piece of work in 8 days and another man can do the same work in 10 days. How long should it take both A and B working together but independently?

Correct option is B

Given:
Man A completes the work in 8 days

Man B completes the work in 10 days
Concept and Formula Used:
Work and time concept:
x is the time for A.
y is the time for B.
t be the time for both A and B
So, for one day work,
​$$\frac1x+\frac1y=\frac1t$$​​
Solution:
Time taken by together to complete the same work be t.
​$$\frac18+\frac1{10}=\frac1t \\\ \\\frac{4+5}{40}=\frac1t \\\ \\\frac{9}{40 }= \frac1t \\\ \\ t = \frac{40}{9 }=4 \frac{4}{9 }$$ days​

Alternate Method: 
Total Work = LCM of 8 and 10 = 40 units

Efficiency of A = 5 unit/day
Efficiency of B= 4 unit/day
Time taken by B to complete the work =$$\frac{40}{9}= 4\frac{4}{9} \text{days}$$​