A person X is twice as good a workman as person Y. By joining together, they complete a job in 18 days. Find the number of days in which X and Y respectively can complete the job if each works separately.

X alone takes 27 days and Y alone 54 days.

X is twice as efficient as Y, so X's rate = 2 x Y's rate.

Together they finish in 18 days, so combined rate = 1/18.

Let Y = r; then 2r + r = 3r = 1/18, so r = 1/54.

Y alone = 54 days and X alone = 1/(2r) = 27 days.

Method: split the combined rate in the 2:1 ratio.