Workdone by A in 1 hour = 1/10 hours
Work left for A and B after 1 hour = 1 - 1/10 = 9/10
Machine A could complete the whole work in 10 hours; it did 1/10 of the work in 1 hour.
Machine B joined Machine A after 1 hour.
With their combined effort, they completed 9/10 of the work in 7 hours.
Let the total time taken for machine B to complete the work = x hours
Machine B will complete 1/x of the jon in 1 hour
Total workdone by the 2 machines in 1 hour => (1/10) + (1/x) = (x+10)/10x
Workdone by the 2 machines in 7 hours to complete 9/10 of the work =>
$$\left(\frac{x+10}{10x}\cdot7\right)=\left(\frac{9}{10}\right)$$
Divide through by 7
$$\frac{x+10}{10x}=\frac{9}{10}\cdot\frac{1}{7}\ =\ \frac{9}{70}$$
By cross multiplying
70 (x + 10) = 9 (10x)
70x + 700 = 90x
20x = 700
x = 34
Therefore, it will take machine B 35 hours to finish the work alone. Hence, option E is the correct option.