If one person can clean a house in 5 hours and second person can clean...

Step 1
Given that one person can clean the house in 5 hours and second person can clean in 4 hours.
House clean by one person in one hours $=\frac{1}{5}$ unit
house clean by second person in one hour $=\frac{1}{4}$ unit
when they work together
Then house clean by both in one hour $=(\frac{1}{5}+\frac{1}{4})$ unit
$=\frac{9}{20}unit$
Step 2
Since $=\frac{9}{20}unit$ cleaning is completed by both in one hours
hence 1 unit cleaning is completed by both in $\frac{1}{(\frac{9}{20})}$ hours
$=\frac{20}{9}$ hours
$=2\frac{2}{9}$ hours
Thus total time taken is $=2\frac{2}{9}$ hours.
Option (c) is correct.