Question 41
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. Working together, they can finish the work in 5 days. Q can do the work alone in:
Solution
Let us assume that P takes 6X days to finish the work.
Q takes 6X/2 = 3X days and R takes 6X/3 = 2X days to finish the same work.
Working together, they take 5 days to finish the work.
==> $$\frac{1}{6X}+\frac{1}{3X}+\frac{1}{2X}=\frac{1}{5}$$
==> $$\frac{1+2+3}{6X}=\frac{6}{6X}=\frac{1}{5}$$
==> X = 5.
Q can do the work alone in 3X i.e. 15 days.
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