X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?

Question: X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?

Solution:
The work rate of X is 1/12 (since X can complete the work in 12 days).
The work rate of Y is 1/18 (since Y can complete the work in 18 days).
In 3 days they complete = 3{(1/12) + (1/18)}
= 3 × (5/36)
= 5/12

Then the fraction of work that is left is = 1 - (5/12)
= (12 - 5)/12
= 7/12