P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?

A) 7

B) 8

C) 9

D) 6

E) Let P takes x days to complete the work

F) Then Q takes x/2 days and R takes x/3 days to finish the work

G) Amount of work P does in 1 day = 1/x

H) Amount of work Q does in 1 day = 2/x

I) Amount of work R does in 1 day = 3/x

J) Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

K) 6/x = 2

L) => x = 12

M) => Q takes 12/2 days = 6 days to complete the work

Question #23884