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