P and Q can do a project in 60 and 30 days respectively. In how many days can they complete 90% of the project if they work together?

Let the total work be the LCM of 60 and 30, which is 60 units.
Calculate their individual efficiencies (work per day):

Efficiency of P =
60
60
​
=1 unit/day

Efficiency of Q =
30
60
​
=2 units/day

Combined efficiency of P and Q working together:

Combined efficiency=1+2=3 units/day
The total project work to be completed is 90% of the total work:

Work to be done=90% of 60=
100
90
​
×60=54 units
Calculate the time taken to complete this work:

Time=
Combined efficiency
Work to be done
​
=
3
54
​
=18 days