P can work thrice as fast as Q. Working independently, Q can complete a task in 24 days. In how many days can P and Q together finish the same task?

Number of days required for Q to complete the task = 24 days

P can work thrice as fast as Q

$$\Rightarrow$$  Number of days required for P to complete the task = $$\frac{24}{3}$$ days = 8 days

Let the total work be W

Work done by P in 1 day = $$\frac{W}{8}$$

Work done by Q in 1 day = $$\frac{W}{24}$$

$$\Rightarrow$$ Work done by both P and Q in 1 day = $$\frac{W}{8}+\frac{W}{24}=\frac{3W+W}{24}=\frac{W}{6}$$

$$\therefore\ $$Number of days required for both P and Q to complete the task = $$\frac{W}{\frac{W}{6}}$$ = 6 days

Hence, the correct answer is Option D